As a few people have mentioned, I avoid online modes in games as a general rule because of stuff like lag and disconnections. However, there's another element that I sometimes have difficulty putting into words. Essentially, when I play a game with friends in the same room I have a sort of camaraderie that I just don't get when I'm playing with people online. It could be the lack of familiarity with the other players, or that I can't actively speak to them, or it could just be that a lot of people in online gaming communities are just dickheads who like to troll or insult other players depending whether they're winning or losing.
I think it was Yahtzee who said, "It's just not the same if I can't reach over and smack somebody for being a douche bag," but I've also noticed that when that's a factor, they aren't even being jerks anyways. Unless you're maybe in an arcade or an actual competition, but I don't go into that sorta thing. I just don't like competitive gaming in general. Much like sports, there's too much hostility from both players and watchers.
I don't play many fighting games anymore. It's true I'm not very good at them, don't have the knack for remembering a billion movesets and combos, plus my reflexes have never been up to par with that sorta genre. I mainly keep to things like Smash Brothers or sometimes Dragon Ball now. Although I used to play Mortal Kombat, King of Fighters, and the various Capcom titles. Still like a lot of the characters and universes they've made for them, I just don't care for the gameplay.