I dont have so much a favourite game but I do have series I look back on fondly (and still play)
For PC it has to be Unreal Tournament (99 and 2k4). Not only for the playability of the vanilla version but also because of the mod capability. Epic pretty much gave away the developers version of the engine in the form of UnreadEd and gave mod/map makers the same tools they used to create the in game environments leading to pretty much infinite replayability (UT99 and 2k4 are in fact making an online comeback)
For Console/PC my choice would have to be Worms. I love the strategic aspect of the game along with the comedy of the characters. Simple gameplay,good looking graphics and online play make this a winner in my book. I still play Worms Armageddon and recently grabbed Worms Evolution on XBLA.