Warning.- I'm quite old school, so if you don't get the reference, please use google etc.
When I think the games I have spend a most time with, there have been so many different types.
At Apple II ... Lode runner (150 levels) and Castle wolfenstein (2D), relatively long games (hours), single player with primitive AI enemies.
At C64 .. so many.. Like M.U.L.E. multiplayer strategy competetive/co-operative game. Numerous arcade-shooters ..
On unix machines Moria, Angband and Nethack. Deep, hard and quite unforgiving
On Amiga .. A lot, way too many to mention (many ideas are from this era). Gfx and Sound become more important, but also the ideas and story likes are more complex.
On Consoles (PS2 and PS3) Metal Gear series game mechanism, hide, don't prefer brute force .. Games like Bioshock and Fallout3 for the atmosphere and storyline. Valkyrie chronicles and Flower.
On PC .. Point&cliks.. some unique ideas like Frozen synapse, Spacechem. Simulators.