TF is as much a game of psychology as of actual gameplay. There are lots of little things you can do to unbalance an opponents team. It's been said more than once that Bard was short for Bastard.... i don't know why :)
Taunts
The inspiration for this would have to be the scene in monty pythons quest for the holy grail where King Arthur is asking for the holy grail which the french invaders have one of already. By taunting the Knights of Camelot they knights charge in to be repelled with catapult launched cows, geese, goats and other assorted farmyard animals. In a similar manner it is possible to influence your opponent to become reckless in their efforts to frag you to show you who is boss. As in real life if you can't defend yourself then maybe you should have shut up in the first place. Particularly effective are the "hey blue, the flags at the other end of the map.... " followed by "if you can get past me you can have it :)". After killing the enemy you can say "Gibs proudly brought to you by --> [DraGoN]Bard <---" or "thanks for the ammo, i used some of mine killing you" or "it's good to be the king" to give them more determination to come rush at you again so you can kill them :).
Grenades
If you are the kind of player that times their grenade perfectly then calmly dodging an enemy's fire and then killing them with a grenade does wonders to an opponents morale. They will not be willing to get close to you and may often run away from you to get into cover. A lot of players use a grenade.wav file which is similar to the one in Q2 so you can time the release better.
Bouncing
Bouncing is using your rocket launcher to bounce an opponent while you are killing them. This makes the opponent feel helpless as they are disoriented and ineffective in combat. If you can keep your cool and are skilled enough this can really ruin an opponents day.
Paranoia by class
A spy is excellent to do this with. On a balcony with snipers become a sniper and drop grenades and pretend to be looking for something else to shoot at across the map. Keep doing this until the snipers start to shoot each other. The next step is to get into the enemy base and toss grenades up from below while you are not there. The enemy will assume one of the snipers there is a spy and will start shooting each other again.
The trap
Most TF players do not look behind themselves as they are moving about. You can use this to your advantage by following an opponent and when they are near to a ledge, lava or something like that you blow them into that area. It is a lot of fun if you know there is a sentry gun up ahead and you are playing TF 2.9. Just as they are about to enter the sentry guns LOS you concuss them and they usually die :)
Blocking ladders and ramps with detpacks
This is a bit of an underhanded tactic which involves using the detpack to block a route to your base. Since you can't blow it up this really annoys some people.