Began playing as an Engineer, mostly out of the desire to support my team mates rather than directly fighting other people.
It was pretty fun when TF2 first came out, back when everyone sucked, no one knew how to fight sentries, and not a single spy was capable of stab n' saps. One sentry gun could get me at least 3 dominations before the game ended. That changed rather quickly though...
My favorite class quickly became Demoman, and it still is. As much as I love supporting my team, keeping them stocked up on ammo and covering their backs with a sentry, I love indiscriminately exploding the bejeezus out of everything in sight. Including myself.
My 2nd favorite would probably be pyro. I love airblasts, axtinguishing, and roasting spies to death (Especially Dead ringer spies, my favorite kind to kill. Fuck 'em.)
I love playing all the classes though. I'm definitely better with some than others (I'm good at being a Demoman, horrible at being a scout) but I will still play each class, as they're all fun and have their uses. I think I have a firm grasp on how each class operates and can be reasonably effective with each class.
I probably have around 400 hours as a Demoman, so I try to stay away from this class and rack up some time on others. Unfortunately, this class is usually empty on the servers I play on and there are usually things that need exploding so... :\