Most of the time I play as a dungeon master, but when I am a player, I often like to pick an oddball class, like a monk or something. (I love monks!) Part of the reason for this is I often like to try something new, so I'll dig up some obscure class I've never tried before and play that. I've played so many RPGs that making my 1000th human fighter or elf mage starts to lose its appeal :p It's also easier to role play something unique than yet another of the same. 3rd edition AD&D did help that a lot, though, with feat choices; you could have two fighters of the same level and race with completely different abilities, whereas in 2nd they were clones.
Sometimes I'll go for 'the character that can do everything'. One friend's campaign (AD&D 2nd edition) I did a half-elf fighter/mage/druid, for
instance. That sometimes has its disadvantages too, like not being able to do anything well, or, in 2nd ed rules, that combo had crappy hp and xp
gain. Still, it was fun to make choices like 'do I heal my buddy, cast magic missile, or attack with a longsword?'
The other thing I'll do, particularly if the group is small, is, like your wife, go for sheer power. The half-ogre barbarian swinging a two-handed
sword, stacked with supporting feats, or the mystic theurge with more spell slots than the rest of the party combined. The drawback to that is
basically I'm picking one thing and taking it to the max, so that when you find a situation where the chosen tactic doesn't work, you become
completely useless. Still, that can be half the fun, complaining about the monster's spell resistance or slash damage immunity or whatever it is
that just screwed you.
Of the basic fantasy classes, though, really I'll play just about anything. Rangers for some reason I don't really like that much. They seem to
suck in a lot of the games I've tried.