For me, I like sports and racing games... I'm not a shoot em up type of guy and RPGs make me feel sick, literally.
Here's my favourite game in each genre would be... and a slight explanation of each genre in case some people don't know:
Action - Action can be action-adventure which features games like say Grand Theft Auto or Zelda... or First Person shooters like Half Life and Halo. For me, I like to play GTA San Andreas...
Fighting - Self-explanitory... one of my favourites is Street fighter...
Role Playing - RPGs aren't my cup of tea but everyone has surely heard of Final Fantasy... Just a question: is Pokemon RPG? I remember the good old days of Pokemon

Platform - Vintage games... 2D... I don't like them either... not my cup of tea... maybe because I was never good at them...
Simulation - This genre includes all types of simulation games... sports of course are included and it includes titles like Sim City too... My favourite is the Live Franchise which is only there cause I love basketball... and yeah, racing is a sub-genre of simulation games...
Strategy - Starcraft is my favourite strategy game only because it was the first game I ever played on a PC.
^^ there are many other genres/sub-genres but this is all I will write...