As been said above it depends on the type etc. and I suppose we ought to be following the advice in the Pilots Operating Handbook/ Flight Manual shouldn't we?
If in doubt under prime since a) less fire risk and b) you know where you are starting from. That said use the oil temp as a guide. If Oil Temp is in the green (talking about PA28/38 here) then do not prime. Oil Temp below green then use 4 to 6 shots depending in conditions.
The PA38 (Mk2) POH says only to prime if engine does not start first time (I wonder whether this is liability in case the engine catches fire on start!) but it also says throttle set half inch for cold start or quarter inch for warm start. It also says leave primer out for cold start and push in whilst cranking.
Sorry but totally disagree with "pumping" throttle on start - quite unecessary and liable to cause many more problems that it will solve.
Whilst on this subject why to some pilots have to keep cranking when it is obvious the engine is not going to start? If you have primed correctly and set the throttle then the engine should start easily first time unless there is something mechanically wrong!