Frans Verbeeck holds the record for most top-10 spots in big races (WCRR, OGRR, Monuments & Grand Tours) without actually winning one with at 0/31. This is far ahead of everyone else. However, Raymond Poulidor did manage to also get 31 top-10's in a row without a victory from after his Vuelta win in 1964 until his retirement.
Most Top-10's without ever winning one
0/31: Frans Verbeeck (all of them in one-day races)
0/21: Michael Boogerd
0/20: Wladimiro Panizza
0/18: Phil Anderson, Severino Canavesi
0/17: Rigoberto Urán
0/15: Romain Bardet
0/14: Fränk Schleck, Michael Matthews
0/13: Adam Yates
Freddy Maertens bears mentioning as he went 0/20 in monuments which is only beaten by Verbeeck's 0/28 in monuments.
We could also include following streaks by cyclists that did win one throughout their careers
31: Raymond Poulidor (26 if GT's are excluded)
25: Herman Van Springel (21 //)
23: Joop Zoetemelk (17 //)
Among active riders Wout Van Aert sits at 15 16 and Alexander Kristoff at 14.
If we only look at GT's we get the following picture
0/12: Joaquim Rodríguez
0/11: Miguel María Lasa, Joaquim Agostinho
0/10: Rigoberto Urán, Fabio Enrique Parra, Wladimiro Panizza, Gianbattista Baronchelli, Mikel Landa
Longest streaks (excl. people that never won one)
13: Alejandro Valverde, Marino Lejarreta
12: Raymond Poulidor
I haven't looked at podiums quite as much.
Most podiums without wins (likely incomplete)
0/8: Frans Verbeeck
0/7: Rigoberto Urán
0/6: Michael Matthews
0/5: Fränk Schleck
Streaks
14: Raymond Poulidor
11: Alejandro Valverde (counting LBL 2010)
9: Felice Gimondi, Wout Van Aert
Streaks (one-day only) (excl. people that never won one)
9: Wout Van Aert
8: Alejandro Valverde (counting LBL 2010), Felice Gimondi
7: Raymond Poulidor (added to show he wasn't missed here)
GT's
0/6: Claudio Chiappucci
0/5: Joaquim Rodríguez
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