Medieval: crossbows and shields (I love shield bashing)
Modern: semi-automatic sniper rifles (I prefer double tapping and triple tapping etc.) and semi-automatic or fully automatic shotguns (there's nothing better than a few million pieces of shrapnel straight to the face).
I tend to avoid using blunt weapons (axes, maces etc.) in medieval games and assault rifles in modern-age games.
Fantasy: Magician, every time. I always play utility characters which can change their role in the game.
Medieval: Assassin style. Best example I can give is playing one of the Splinter Cell games... instead of playing the game like most people, I went and literally only killed three characters I was forced to kill on the hardest setting. (Took me forever to do lol.)
WWII: Bolt action rifles and sniper rifles
Modern: Sniper rifles, assault rifles, pistols
Racing games (lol): all wheel drive of rear wheel drive ftw. I hate FWD cars. Also generally prefer to play class D - B, anything faster gets rather silly. Skylines are probably my favorite, but cliche I like Supras 'cause they drive like my old Toyota Soarer (SC 300) I once had.
I generally stopped playing most intense games recently, but in the two most recent my mains were wizard characters. I played Counter Strike and Counter Strike Source to the point the game became humorous to me. I was so good, I was frequently banned from most servers I played on for hacking. On numerous pub games I'd do crazy shit like take 10+ people vs. me successfully.