There are a lot of good ones!
For shooters my favourite is TimeSplitters 2. Loved playing that. Especially great if you had a friend with one of those 4 controller splitter things so you could do 4 player split-screen. Add in some bots too and you've got a great game going. So many options in the game as well. Honourable mentions to Perfect Dark, similar concept just not quite as refined, and Halo 3, crap in the deathmatch kind of area (no bots? WTF!?) but playing the campaign in split screen was insanely good.
For sports games, FIFA no contest. It's a shame that it's gotten worse in terms of local MP over the years though. People often complain about the lack of career mode improvements, but back in 03 you could do a local MP career mode with different teams for each player. So it's not just that career mode hasn't been improved, it's that it's actually gotten worse. If I were to name a single FIFA game as the "best" one for local MP though I'd say the 2010 FIFA World Cup game. Being able to play a local MP game right from qualy to the final was awesome. Plus IIRC that version had a load of cheat options too, so even if you just wanted to play a few one off matches you could have some good fun there.
For racing games I'd say Mario Kart Wii. Had a lot of fun playing that. Would also put Grid 2 right up there, although I'd give the edge to MK.