As someone who hasn't played every game in the series ill try my best 5 based on what i have played (this will be my favorites so bare with me!)
Resident Evil 3
Resident Evil Revelations
Resident Evil 1 (remake on the Gamecube)
Resident Evil 4
Resident Evil 2
I've played them all but 6,Mercs,ORC and the Wii versions.