My boyfriend and I don't get along when we play games together.
Tales games together? He free-runs all the time and doesn't help out with combos. It also doesn't help that I generally play on a higher difficulty than he would like.
Fighting games? We're both super-competitive. He button-mashes in games he's not familiar with (and combos when he does know the game) I try to combo and sometimes it's successful and sometimes it isn't.
Platformers? Depends. We had a rough hilarious ride with NSMB Wii with us throwing each other into pits. Actually, we're alright with Mario games. Platformers are alright.
I can't play first-person shooters with him because they make me nauseous.
Dumbass trivia / minigame / nonsense games? We get a laugh out of the absurdity even though the games may not be that great.
We're better off watching each other play games, to be honest. Or taking time to ourselves and playing on our own (ex: he does it with God of War, hockey games/WWE stuff, shooters, and RPGs; I do it with RPGs, platformers, and action/adventure games).
Edit: I just can't fathom playing SP games with him and switching off after every mission/dungeon/level, though (outside of SMB3, which did that sort of thing decently). We play games far too differently from each other. He grinds in RPGs. I don't. He likes to take his sweet time in platformers. I like going fast. He likes button-mashing in fighters; I don't. He likes free-running in Tales; I can't stand the mechanic. It's just somethin' you've gotta come to grips with. And those differences, even if they're irritating at times, are what makes things exciting.