I know a lot of people are big on the wide tyres (25's+) but after giving it a go I think if your rimsa re narrow the 23 is a good job, I didn't get any less flats myself, actually ythis has been a worse year than the last couple but that is just pot luck.
Gatorskins, GP4Seasons for Conti, or Swalbe Blizzard have all done me well, I think the Gators are probably the best.
I ride hard and over everything including steps and dirt. I rate Specialized Armadillo Elites. Heavy (comfy), fast enough and strong as you get! Ive even raced em in Div1 one.
For really ****ty weather training I use armadillo's in 25mm. These cope fine with dirt roads and deal really well for embedded glass and the like. They are heavy and a little dead feeling but as Durainian says they are racable if you are keen.
If you are just looking for a good all round tyre through I cant go past folding vitorria rubino pro's in either 23 or 25mm. 23's are a great rough weather racing tyre as well as fast training, but the 25's are perfect for longer training rides and they offer pretty good punture resistance without the heavy feel of the armadillo's