It depends on the game, for me. Usually it's the weapon that is the most versatile. In Rainbow Six Vegas I use a G36 about 90% of the time, because even if it's not always the best in a given situation, it's never useless. I am sad about my poor, rickety fast-shooting AKM-74 in STALKER right now, because even though it's starting to jam all the time from overuse, I miss its ability to get me out of almost any situation, and how silly it looks with its grenade launcher and scope monopolizing the right side of the screen. I will have to have a 21-gun salute with a lesser weapon when it finally becomes too unreliable to use.
Halo 3 doesn't have a gun like this, so I always try to get the best weapon for the situation, and as soon as that situation changes, I get a new one. I rarely hold onto a 'good' weapon if I don't think I will use it very soon. If people are using sniper rifles, I will not hesitate to toss the sword aside for my own sniper rifle. The only exception is Snowbound (I think that's what it's called), where I'm an unapologetic shotgun whore.
I play a Heavy in TF2 because his minigun is useful against pretty much anything besides a Sniper. Again, vesatility is the big things for me, i hate getting caught with my pants down.
Games where you can carry an armory in your coat pocket are not as common anymore, but in such games I still follow this way of thinking, along with a tendency to use whatever has the most plentiful ammo. The shotgun in Doom 3, sometimes to the point I forgot I had more appropriate weapons after letting them gather dust for so long, and the SMG in Half-Life 2, except when AR-2 ammo was plentiful or really big baddies showed up.