Here's a rundown of each of the major BB systems currently available, along with advantages, disadvantages & notes on compatibility.
Conventional threaded
Modern threaded bottom brackets are not a new invention.
The idea is simple: by moving the bearings outboard of the shell, you can then use a much larger spindle. Currently, 24mm is the accepted norm compared to square taper's relatively miniscule 17mm diameter.
Shimano popularized the concept as Hollowtech II, with the introduction of the XTR M960 group in 2003 – even now it's still, arguably, the gold standard.
Pros: Easy at-home service; interface surfaces can often be machined; huge selection of parts and accessories
Cons: Heavier than press-fit systems; frame design limited by relatively small-diameter and narrow shell
Crank designs that will fit: Standard 24mm external type (Shimano Hollowtech II, SRAM/Truvativ GXP, Campagnolo Ultra-Torque, FSA MegaExo, Race Face X-Type, etc), square taper, ISIS, BB386 EVO
BB90/BB95
Trek introduced BB90 in 2007, on the revamped Madone, and soon followed with the mountain bike-specific BB95. Instead of having cartridge bearings that were pressed into aluminum cups that were then threaded into the frame, Trek eliminated the middle man and pressed the bare bearings directly into the frame.
Bearing seats were molded into the carbon fiber frame structure, to save weight, and bottom bracket shell width ballooned to 90mm on road bikes and 95mm on mountain bikes, creating more real estate for frame tubes and suspension pivots.
Aside from omitting the cups, the BB90/95 setup is functionally identical to conventional threaded bottom brackets, in that it uses the same bearings and the same bearing locations as before. Crankset compatibility is thus unchanged, although you do lose the ability to run chain guides that sandwich between the driveside cup and frame.
Trek's adherence to the standard it created seems to be wavering, though, as many of the models introduced for 2016 have switched to PF92 (which is covered below).
Pros: Lighter than conventional setups but retains wide range of compatibility; creates a wider BB shell without affecting crank width
Cons: Can't use cup-mounted chain guides; shell is wider but still small in diameter; requires a separate bearing puller and press for service
Crank designs that will fit: Standard 24mm external-type only
PF86/92
Very closely related to Trek's BB90/95 system is the PF86/92 standard used by Scott, Giant, Pivot, and many others. Once again, the bearings and their locations in space are identical to those of conventional threaded bottom brackets, only they're mounted in small composite cups before being pressed into the frame.
The advantages are similar to those for Trek's BB90/95: a wider bottom bracket shell that doesn't otherwise affect crank width, plus lighter weight compared to threaded aluminum cups.
From a manufacturing standpoint, PF86/92's dimensional tolerances aren't as stringent as BB90/95's, and it's easier to adapt the system into aluminum frames. As long as you have a concentric bore of the right diameter, parallel faces, and a proper shell width, you're good to go.
Pros: Same as BB90/95
Cons: Same as BB90/95
Crank designs that will fit: Standard 24mm external-type, BB386 EVO
BB30
Several companies have dabbled in alternative bottom bracket standards over the years (Gary Fisher, Klein, and Merlin, to name just three) but it wasn't until Cannondale released its then-proprietary BB30 system as an open standard in 2006 that something actually stuck.
BB30's bearing cartridges press directly into a precision-fit shell, as with Trek's BB90/95 system – albeit with the additional aid of two pairs of snaprings. But here it's the shell and spindle diameters that increase in size, not the shell width.
The key benefits here are lighter weights owing to the larger, 30mm-diameter aluminum spindle and the elimination of separate bearing cups. Plus, because the shell is still just 68mm wide, the cranks can also be made to provide more heel clearance – or, depending on the crank design, even a narrower stance width (commonly referred to as 'Q factor').
BB30 shells, however, do require more stringent dimensional tolerances to work well – meaning it's more expensive to manufacture. Moreover, with the notable exception of Felt, who uses a carbon tube, BB30 also usually employs an aluminum shell insert that has to be bonded or co-molded into an otherwise carbon fiber frame.
Pros: Lighter weight; more resistant to axle twist; more heel clearance; larger-diameter shell and spindle; potential for narrower pedal stance width
Cons: Shell still just 68mm wide; metal-on-metal interfaces can be prone to creaking; requires a separate bearing puller and press for service; requires high manufacturing tolerances; bearing seats can't easily be faced post-manufacturing
Crank designs that will fit: BB30, BB386 EVO, standard 24mm external-type, Specialized OSBB, BBright
BB30A
Cannondale has a variant of BB30 called BB30A. This uses a shell that's 5mm wider than the original but it's an asymmetrical layout that only adds those extra millimeters on the non-driveside. According to Cannondale, this allows for wider bearing spacing and better spindle support (which should improve bearing longevity). Other critical dimensions such as bearing outer diameter and thickness remain unchanged, and there's also no difference in pedal stance width or ankle clearance (in most cases).
Those extra five millimeters can complicate crank compatibility, however. BB30-compatible cranks that feature axle spacers on the non-driveside (such as from Cannondale and SRAM) will work just fine, as all you'll have to do is remove spacers as needed to accommodate the extra width, but BB30 cranks without such spacers (such as from FSA and Specialized) won't work. Thankfully, many newer BB30-compatible cranks now feature extra-long spindles for wider compatibility and those will install just fine.
Pros: Lighter weight; more resistant to axle twist; more heel clearance; larger-diameter shell and spindle; potential for narrower pedal stance width
Cons: Metal-on-metal interfaces can be prone to creaking; requires a separate bearing puller and press for service; requires high manufacturing tolerances; bearing seats can't easily be faced post-manufacturing; not all BB30 cranks will fit
Crank designs that will fit: BB30 (some), BB386 EVO, standard 24mm external-type, BBright
PF30
SRAM addressed BB30's stringent dimensional tolerances and their associated manufacturing costs with the advent of PressFit 30 in 2009. Just as with PF86/92, PF30 is analogous to BB30 in that the bearings and bearing locations are identical, but with the addition of intermediary composite cups that allow for looser frame tolerances.
The Specialized OSBB system
The OSBB is basically the same as BB30 but with a little tighter tolerances and a 0.5mm difference in the clip-to-clip dimension. Cranks of both systems are compatible with each other.
Pros: Same as BB30 but with lower costs, easier assembly, and the potential for additional bearing seals integrated into the cup/bearing assembly
Cons: Standard-width shell; requires a separate cup remover and press for service
Crank designs that will fit: BB30, BB386 EVO, standard 24mm external-type, Specialized OSBB, BBright
BBright
BBright shares its 30mm-diameter aluminum spindle, cartridge bearings, and driveside bearing location with PF30 – in fact, the bottom bracket cups are identical to PF30.
However, the non-driveside bearing is pushed outward by 11mm – the same as conventional threaded, BB90, and PF86 bottom brackets. This makes it something of a hybrid between the two widely accepted systems.
Pros: Stiffer than BB/PF30, in theory, without impacting other attributes; good crank compatibility, cheaper to manufacture than threaded or BB30
Cons: Questionable longevity; requires a separate cup remover and press for service
Crank designs that will fit: BBright, BB386 EVO, standard 24mm external-type
BB386 EVO
Takes the oversized principle to extremes. The bearings have the same nominal spacing, width-wise, as conventional threaded, BB90/95, and PF86/92 formats, but it uses BB/PF30's bigger 30mm diameter spindle.
As stiffness is directly tied to cross-sectional size it's no surprise that, theoretically, BB386 EVO has the most to offer, with both the added shell width and diameter that many frame-makers yearn for.
In addition, it uses the same bearings and cups as PF30 and BBright and, thus, the same manufacturing tolerances and required tools.
Pros: Theoretically the best in terms of frame stiffness; reduced manufacturing costs; generous crankset versatility
Cons: Heel clearance isn't as good as BB30; requires a separate cup remover and press for service
Crank designs that will fit: BB386 EVO, standard 24mm external-type
Conventional threaded

Modern threaded bottom brackets are not a new invention.
The idea is simple: by moving the bearings outboard of the shell, you can then use a much larger spindle. Currently, 24mm is the accepted norm compared to square taper's relatively miniscule 17mm diameter.
Shimano popularized the concept as Hollowtech II, with the introduction of the XTR M960 group in 2003 – even now it's still, arguably, the gold standard.
Pros: Easy at-home service; interface surfaces can often be machined; huge selection of parts and accessories
Cons: Heavier than press-fit systems; frame design limited by relatively small-diameter and narrow shell
Crank designs that will fit: Standard 24mm external type (Shimano Hollowtech II, SRAM/Truvativ GXP, Campagnolo Ultra-Torque, FSA MegaExo, Race Face X-Type, etc), square taper, ISIS, BB386 EVO
BB90/BB95

Trek introduced BB90 in 2007, on the revamped Madone, and soon followed with the mountain bike-specific BB95. Instead of having cartridge bearings that were pressed into aluminum cups that were then threaded into the frame, Trek eliminated the middle man and pressed the bare bearings directly into the frame.
Bearing seats were molded into the carbon fiber frame structure, to save weight, and bottom bracket shell width ballooned to 90mm on road bikes and 95mm on mountain bikes, creating more real estate for frame tubes and suspension pivots.
Aside from omitting the cups, the BB90/95 setup is functionally identical to conventional threaded bottom brackets, in that it uses the same bearings and the same bearing locations as before. Crankset compatibility is thus unchanged, although you do lose the ability to run chain guides that sandwich between the driveside cup and frame.
Trek's adherence to the standard it created seems to be wavering, though, as many of the models introduced for 2016 have switched to PF92 (which is covered below).
Pros: Lighter than conventional setups but retains wide range of compatibility; creates a wider BB shell without affecting crank width
Cons: Can't use cup-mounted chain guides; shell is wider but still small in diameter; requires a separate bearing puller and press for service
Crank designs that will fit: Standard 24mm external-type only
PF86/92

Very closely related to Trek's BB90/95 system is the PF86/92 standard used by Scott, Giant, Pivot, and many others. Once again, the bearings and their locations in space are identical to those of conventional threaded bottom brackets, only they're mounted in small composite cups before being pressed into the frame.
The advantages are similar to those for Trek's BB90/95: a wider bottom bracket shell that doesn't otherwise affect crank width, plus lighter weight compared to threaded aluminum cups.
From a manufacturing standpoint, PF86/92's dimensional tolerances aren't as stringent as BB90/95's, and it's easier to adapt the system into aluminum frames. As long as you have a concentric bore of the right diameter, parallel faces, and a proper shell width, you're good to go.
Pros: Same as BB90/95
Cons: Same as BB90/95
Crank designs that will fit: Standard 24mm external-type, BB386 EVO
BB30

Several companies have dabbled in alternative bottom bracket standards over the years (Gary Fisher, Klein, and Merlin, to name just three) but it wasn't until Cannondale released its then-proprietary BB30 system as an open standard in 2006 that something actually stuck.
BB30's bearing cartridges press directly into a precision-fit shell, as with Trek's BB90/95 system – albeit with the additional aid of two pairs of snaprings. But here it's the shell and spindle diameters that increase in size, not the shell width.
The key benefits here are lighter weights owing to the larger, 30mm-diameter aluminum spindle and the elimination of separate bearing cups. Plus, because the shell is still just 68mm wide, the cranks can also be made to provide more heel clearance – or, depending on the crank design, even a narrower stance width (commonly referred to as 'Q factor').
BB30 shells, however, do require more stringent dimensional tolerances to work well – meaning it's more expensive to manufacture. Moreover, with the notable exception of Felt, who uses a carbon tube, BB30 also usually employs an aluminum shell insert that has to be bonded or co-molded into an otherwise carbon fiber frame.
Pros: Lighter weight; more resistant to axle twist; more heel clearance; larger-diameter shell and spindle; potential for narrower pedal stance width
Cons: Shell still just 68mm wide; metal-on-metal interfaces can be prone to creaking; requires a separate bearing puller and press for service; requires high manufacturing tolerances; bearing seats can't easily be faced post-manufacturing
Crank designs that will fit: BB30, BB386 EVO, standard 24mm external-type, Specialized OSBB, BBright
BB30A
Cannondale has a variant of BB30 called BB30A. This uses a shell that's 5mm wider than the original but it's an asymmetrical layout that only adds those extra millimeters on the non-driveside. According to Cannondale, this allows for wider bearing spacing and better spindle support (which should improve bearing longevity). Other critical dimensions such as bearing outer diameter and thickness remain unchanged, and there's also no difference in pedal stance width or ankle clearance (in most cases).
Those extra five millimeters can complicate crank compatibility, however. BB30-compatible cranks that feature axle spacers on the non-driveside (such as from Cannondale and SRAM) will work just fine, as all you'll have to do is remove spacers as needed to accommodate the extra width, but BB30 cranks without such spacers (such as from FSA and Specialized) won't work. Thankfully, many newer BB30-compatible cranks now feature extra-long spindles for wider compatibility and those will install just fine.
Pros: Lighter weight; more resistant to axle twist; more heel clearance; larger-diameter shell and spindle; potential for narrower pedal stance width
Cons: Metal-on-metal interfaces can be prone to creaking; requires a separate bearing puller and press for service; requires high manufacturing tolerances; bearing seats can't easily be faced post-manufacturing; not all BB30 cranks will fit
Crank designs that will fit: BB30 (some), BB386 EVO, standard 24mm external-type, BBright
PF30

SRAM addressed BB30's stringent dimensional tolerances and their associated manufacturing costs with the advent of PressFit 30 in 2009. Just as with PF86/92, PF30 is analogous to BB30 in that the bearings and bearing locations are identical, but with the addition of intermediary composite cups that allow for looser frame tolerances.
The Specialized OSBB system

The OSBB is basically the same as BB30 but with a little tighter tolerances and a 0.5mm difference in the clip-to-clip dimension. Cranks of both systems are compatible with each other.
Pros: Same as BB30 but with lower costs, easier assembly, and the potential for additional bearing seals integrated into the cup/bearing assembly
Cons: Standard-width shell; requires a separate cup remover and press for service
Crank designs that will fit: BB30, BB386 EVO, standard 24mm external-type, Specialized OSBB, BBright
BBright

BBright shares its 30mm-diameter aluminum spindle, cartridge bearings, and driveside bearing location with PF30 – in fact, the bottom bracket cups are identical to PF30.
However, the non-driveside bearing is pushed outward by 11mm – the same as conventional threaded, BB90, and PF86 bottom brackets. This makes it something of a hybrid between the two widely accepted systems.
Pros: Stiffer than BB/PF30, in theory, without impacting other attributes; good crank compatibility, cheaper to manufacture than threaded or BB30
Cons: Questionable longevity; requires a separate cup remover and press for service
Crank designs that will fit: BBright, BB386 EVO, standard 24mm external-type
BB386 EVO

Takes the oversized principle to extremes. The bearings have the same nominal spacing, width-wise, as conventional threaded, BB90/95, and PF86/92 formats, but it uses BB/PF30's bigger 30mm diameter spindle.
As stiffness is directly tied to cross-sectional size it's no surprise that, theoretically, BB386 EVO has the most to offer, with both the added shell width and diameter that many frame-makers yearn for.
In addition, it uses the same bearings and cups as PF30 and BBright and, thus, the same manufacturing tolerances and required tools.
Pros: Theoretically the best in terms of frame stiffness; reduced manufacturing costs; generous crankset versatility
Cons: Heel clearance isn't as good as BB30; requires a separate cup remover and press for service
Crank designs that will fit: BB386 EVO, standard 24mm external-type