Looking back, I've noticed it changes along with how I view myself in reality. So over the course of about 10 years it went pure mage -> pure stealth -> mage/stealth hybrid. I'll spare you the underlying life story.
That's just for the cases where player class is a fairly fluid thing though, a la skyrim. If it's a more rigid affair, like WoW, I'm currently attracted to anything that is hybrid, exotic, rare (in MMO's), skill-based, highly mobile, DPS heavy, involves dual wielding, involves guns, ... The list goes on for quite a while, but the general idea is this: the less it looks and plays like a traditional warrior the better. Which is odd because I know all too well how fun it can be to just wade into things with a giant sword, but I guess you can't argue tastes. Not even your own.
The most enjoyable pre-made class I've ever played was my guild wars 2 elementalist and for non pre-made my mage gunner fran in final fantasy XII. Honorable mention goes to my pistols only sniper in XCOM - enemy unknown. There may have been no sane reason to do it, but I'll be damned if he didn't look cool doing it!
In FPS though, it's hard to say. In TF2 for example I bounce between pretty much anything except engineer and medic because I find them very boring. And if available my first choice will always be scout, soldier, sniper or spy. So I guess the theme here is mobility and/or stealth?