Lots of ppl buy stock cars and race them on the street.... they may have a lot going against them but they do it.... many cars are decently fast stock for stoplight races, if you're talking about dragstrip then hell no, unless they have a Viper or something....
Typical cars that fall in this category:
V8 F-bodies and Mustangs, Supra, 300zx, RX-7, NSX, 3000GT, S4, Vipers, Porsches, some Bimmers, etc... all can run 14s and lower, which isn't bad for bone stock and street tires...
Typical cars that kids try to race stock but aren't fast:
Civics (especially SI), Integras (except Type R), V6 F-bodies and Mustangs, non-turbo eclipses