Depends on the game and the amount of times I've lost to a person.
In Pokémon, it's not much of a big deal if I lose to someone even repeatedly (never was a good competitive battler), but I get excited if I win against someone good.
In Smash Bros, I shrug off the occasional win as luck, but if it repeats then I change tactics or admit they might be good.
In Halo, every now and then I ragequit (not often, though) ESPECIALLY if there's intentional friendly fire. Ugh, I hate those people. If they're gonna kill someone, let it be the other team, not your teammate who happened to respawn next to you.
In any other FPS, I get a little flustered but generally maintain my composure. Chances are, I'm not too good in what I'm playing (such as Team Fortress 2).