My favourite tactic is as a medic:
When with a class that can take a lot of damage, or a player who is good at distracting enemies.
Wait until you're both close to the enemy then leap diagonally round to the side of the enemy that they are not looking, and hack them to death with your saw.
Extremely effective on soldiers, also killed a few heavies with it, don't try it on a pyro.
This requires a lot of jumping, strafing, and a decent ally, a distracted enemy, and/or a lot of luck. Extremely effective on soldiers who have just rocket jumped, even with no distraction.
Edit: Jumping over someone whose climbing stairs, from the top of the stairs, is also effective for this.