Anti-Medic strategy

“

Sorry there nurse, I mistook ya for an actual threat!

Click to listen

— The Sniper

”

The Medic moves quickly and has a decent amount of health, but is poor at self-defense, requiring the protection of his healing partner and team to survive.

General

The Medic should always be top priority when you are considering whom to kill. A team without their Medic is at a severe disadvantage.
The Scout's Force-A-Nature knockback and the Pyro's airblast can be used to disconnect enemy Medics from their partners, or vice versa.
It's always best to disconnect and isolate the Medic to prevent him merely latching onto another team-mate, especially during an ÜberCharge.
When fighting a Medic and his healing partner, try to kill the Medic instead. His partner will merely shrug off your damage.
As a Sniper, it is easier to bodyshot the Medic then go for a headshot. A fully charged bodyshot will kill in one hit, granted the Medic is not overhealed.
As a Spy, disguise as an offensive class, preferably Heavy, Demoman, or Soldier, then try to lead the Medic to his death.

Weapon Specific

A list of useful tidbits about the Medic's tools, and how to best counter them.

Syringe Gun

Blutsauger

Crusader's Crossbow

The Crusader's Crossbow deals damage based on how far away the target is. Closing the distance will make it deal less damage.
The bolts fired from this crossbow heal the Medic's allies. Consider taking a shot if it means denying someone a quick heal.
The Crusader's Crossbow has a slow firing rate. Take advantage of this by countering between shots.