I'm one of the rare players that will do any and everything for his team. I will take up any roll that the team is low on and will perform the duties as best as I can. My play-style, though, is ultra-aggressive across the board. I love to push and will continually lead the charge into enemy territory with reckless abandon. My tactics with each class are as follows.
Scout - I will hit and run enemies and try to complete objectives when I can. In open maps like Granary, Turbine, Gravelpit, and Fastlane I like to circle around and attack Heavy/Medic combos and pick off Snipers and Demos where they are camping. I will also attack Soldiers aggressivly, using double-jump and evasion to kill them. In close-quarters maps I usually like to attack enemies from behind or the side if possible, I'll pass up killing to complete the objective though.
Soldier - As a soldier there is never a moment where I'm not moving forward. I will attack any and all enemies regardless of class. I like to Rocketjump to change levels and attack from above if I can. I also like to clear and capture points.
Pyro - I typically assist teammates by airblasting projectiles away and putting fires out. I also like to harass Scout, Engineers, Snipers, and Spies by setting them on fire with my flare gun and leaving them to burn. I'll take on Soldiers and Demos but will usually pass on Heavies.
Demoman - I usually pick a point to choke the enemy and will take out as many enemies as I can before I move to another point. I target engineers and their buildings first and foremost. I love to kill scouts with the grenade launcher, it's just a satisfying kill.
Heavy - I run around screaming for a medic and lead both of us into the enemy spawn.... No seriously. I like to take the lead and have my teammates follow behind me, the sound of my minigun usually indicates a whirling, bullet-riddled doom for the other team. I usually act as team captain when I'm a heavy.
Engineer - Much like the demo I will find a chokepoint and camp it to all hell. I tend to be a defensive engineer so I'll usually build around the spawn or intel (if playing CTF.) I like to mix things up sometimes and place my sentry in enemy territory as an act of defiance. =D
Medic - As a medic I focus on hurt or burning players first, then I will heal Heavies, Soldiers, and Demos. Next are Pyros, Snipers, Snipers, and Spies, finally Scouts. I'll overheal all teammates I pass so Engineers will get healed sooner or later. I usually use the normal Medigun with the Blutsauger and Ubersaw. I'm a pretty basic medic but it gets the job done.
Sniper - I'm a bit of a tricky sniper. I don't have good "aim" but I have good reflexes and have a good twitch shot, so I can pull off some ridiculous shots if given time to set up. I also like to snipe in unexpected places. The hallway between Spawn and C/L at Blackmesa has seen me snipe a few enemies. I'm generally not good in 1v1 sniper battles, so I tend to move around to a lot of different places to throw enemies off.
Spy - I do the basic spy stuff, run around sapping sentries and stabbing baddies. I use a lot of different tactics as a spy. If I told you all of them I'd have to kill you...but I'd probably do that anyway. =P