If you can stay away from your namesake and take the Spy hunter's check-shots unflinchingly, the challenge becomes to act like an enemy. We like to dress up as a Heavy, because his reassuringly enormous size makes it hard for anyone to believe he could be a slinky Spy in disguise. It also means you get healed by enemy Medics - a peculiar sensation - and that can lead to an utterly bizarre psychological dance.
The Spy, you see, needs to get behind his victim for a one-hit-kill backstab. The Medic, meanwhile, should always stay behind a Heavy for protection while he heals. So the two of you run in circles trying to get behind each other, until the Medic realises - with an almost visible pang of horror - who you really are. He draws his bonesaw, you draw your butterfly knife, and the duel commences. It's sublime. The knife-edge between the thrill of deception and the shame of discovery makes playing a Spy more tense and thrilling than any other multiplayer experience - even the original TF's Spy.
The other class highlights are more obvious: shredding a dozen enemies as a Medic-boosted Heavy, bolting past a superior force as a Scout with the briefcase in 2Fort, and detonating enough pipe bombs as a Demoman to fill the room with blood - and the screen with kill reports. In fact, the only class that doesn't excite is the Medic. His contribution is to heal the major players while they charge in, but he can't do anything else while he heals so his whole life is just holding down fire. When he's healed a thousand or so points, he can temporarily make himself and his mark invulnerable, at which point he has to... keep holding down fire. It's so cruel that he doesn't get to let rip after all that joyless service to his team.