Racing
Burnout Series: I racing game that focuses on causing crashes? I can do that! While I hated 75% of the game for simply being normal races, I did love the "Cause the biggest wreck possible" events.
Need for Speed - Hot Pursuit: Racing AND Avoiding the police? Driving a police Lamborghini? Awesome. This was great fun when it first came out.
Sports Games
NFL Blitz - All the fun an strategy of a normal football game, but with the added fun of throwing people 10 yards instead of simply tackling them.
NBA Jam
Any NON-REALISTIC sports game
RTS
Command and Conquer - I hated how quickly I got overwhelmed in Starcraft. My early game was near perfect, but once I need to focus on building units as well as MULTIPLE structures I start showing how unskilled I am. C+C you can only build 1 building, 1 infantry, 1 vehicle, 1 plane, and 1 boat as the same time. That I can handle. I'm still not good in multiplayer, but I never was.
Realistic WW1/WW2/Modern Military Shooters
Call of Duty 4: Modern Warfare - There was a reason this was GOTY(Wasn't it?). The standard gameplay you'd expect from a modern war shooter, with just enough variety to keep it fresh. Oh, and the Nuke scene...
MOBA
League of Legends - I hate DOTA, I don't like DOTA 2, and I dislike 90% of games that try to emulate this kind of play. However, I am decent at LoL. Might be that I had some friends to play with, might be that they removed some of the counter intuitive ideas from DOTA (Denying for example, I still can't wrap my head around getting rewarded for killing your own units), but I still enjoy the occasional game (though I only have about 500 under my belt, and I've been playing since Season 1)