Class, generally no. Archtype, in a sense. In RPGs I play the person that wields one sword, not with a shield, not akimbo swords, not a two hander, and not anything that's not a sword; but a sword. And is damn good at using it. Rather than playing as a "Warrior" per say, I play as a Blade Master. And in FPSes, I don't generally play as the Assault, or Soldier class; but I play as the Recon/Pointman class, or Sniper/Marksman class and use them in a very up-front combat-heavy way. For example: Bad Company 2, Recon (Sniper-type class) with a shotgun. And without slugs...I'd prefer Magnum Ammo and more grenades/motion mines or movement speed (Depending on map), thank you.
Why play the sniper in an assault position? Simple: First, he's a Recon, not a Sniper. More fitting. Second, it's an excuse to use a pump-action shotgun and that revolver magnum I love oh-so very very much. Third, I get a gillie suit and what seems like quieter movement noise (I hear it less in-game, and people seem to flip about and blast me while I'm closing distance less often.), so I get the elements of stealth and surprise. Fourth, I get mortars/C4, and that's OK by me. Fifth, motion mines. Beeps whenever there's an enemy in it's radius (Great for making sure bases/houses are clear of bad guys), and you get bonus points if someone kills an enemy in it's radius. With this set-up I get to act like a lone wolf, force multiplier, personal assault, and support operator all in one; and rather effectively, too.