My favorite was the pyro. A powerful class with annoyingly good capabilities. I would use the distinguisher (the fast switch main) and axetinguisher (the burn crit axe). I would secondary attack then use the shotgun or reserved shooter
Valve nerfed the shit out of the pyro class long time ago, though. Distinguisher switches slower and now the axtinguisher does mini crit instead of crit.
My another class is the soldier, mostly because I have the FDU and soldier is a pretty easy class with well rounded capabilities.
Spy for fun play (I don't think the spy is a very good class unless you're very good at it), using my C&D to sneak behind enemy line and sabotage sentries with RTR
Scout for fast paced gameplay. He's fast and fun. Good when you're impatient and scout is the best class for practising aim.
My misc classes
Sniper with huntsmen or to get rid of enemy snipers or on fullcrit server (cause noscope is accurate)
Heavy to get rid of spawncampers
Medic for support
Demoman to spam shit into covered enemy