I'll break it down by sub-genres:
In JRPG's my favourite one is a Monk. High damage, high HP count, great evasion. Oh, and sometimes monks have something beyound just damage dealing, like self heal, or posion-removing skill. The fact that they fight with their fists adds to coolness. Yeah, as soon your warrior gets his/her late game equipment, the importance of monk fades, but I still bring them to the final battle.
I hadn't played too many ARPG's, but judging by the way I play Engineer in Torchlight 2, in those games I like tanky guys that can deal a lot of AoE damage.
As for traditional WRPG's, I'd say whichever class is the best at persuasion. If any PC class can become the persuation master, then I'll go for someone with big mace, tons of HP and heaviest possible armor. Probably because dealing with all the magic is more of a hassle then enjoyment. Why would I pick mage if most spells are useless (as it is in most cases) and I'll end up just throwing trusty fireballs if I can pick warrior and just hack it out? Only for roleplaying reasons, probably.
But if it is a "free-class" WRPG (like Shadowrun, Or Arcanum) I'll always make someone persuasive, with a single weapon specialization (preferably ranged) and something for fun (decking in Shadowrun, for example) with maybe some abilities for summoning additional aid.
I'd also like to make a special mention towards classes/characters that can fight in close range AND be healers.