Below are all the items classes can use to self-heal. Every single class has some sort of self-healing.

Scout

• Mad Milk
  • returns 60% of damage done to soaked enemies as healing for self and allies
• Candy Cane
  • If the scout kills an enemy (even without the Candy Cane, as long as the Candy Cane is equipped) the enemy's body drops a small health kit

Soldier

• Concheror
  • on use, returns 35% of damage done as healing for self and allies within a radius
• Black Box
  • each successful hit yields +15 hp per enemy hit
• Half-Zatoichi
  • upon kill, heals 50% of the killed enemy's max hp (and can overheal).
    (Note that if holstered/switched away without a kill, 50 health will be deducted from the player's current health. If the player is below 50 health points, the weapon can not be holstered until the player gets a kill or they get more health).

Pyro

• Phlogstinator
  • upon full "Mmph!", taunting grants full hp, damage resistance, and guaranteed critical hits
• Powerjack
  • restores +75 hp with kill

Demoman

• Persian Persuader
  • any ammo picked up from boxes or weapons is converted into health
  • dispensers provide no ammo, but resupply cabinets still do
• Eyelander/Nessie's Nine Iron/Horseless Headless Horsemann's Headtaker
  • each successful kill increases speed by 8%, max hp by 15, and heals for 15
• Half-Zatoichi
  • upon kill, heals 50% of the killed enemy's max hp (and can overheal).
    (Note that if holstered/switched away without a kill, 50 health will be deducted from the player's current health. If the player is below 50 health points, the weapon can not be holstered until the player gets a kill or they get more health).

Heavy

• Sandvich
  • heals +300 hp over 4 seconds.
• Dalokohs Bar/Fishcake
  • heals and increases max hp by 50 for 30 seconds

Engineer

• Dispensers
  • Level 1: +10 hp per second
  • Level 2: +15 hp per second
  • Level 3: +20 hp per second

Medic

• Automatically heals +3 hp per second
• Blutsauger
  • heals +3 hp every successful hit, but drains -2 hp per second
• Kritzkrieg
  • Oktoberfest taunt heals self +11 hp
• Quick Fix
  • while using ÜberCharge, heals patient and medic +100.8 hp per second or +302.4 hp per second if out of combat
• Amputator
  • while taunting, heals all allies at +25 hp per second (or +75 hp per second if out of combat) within a certain radius for 4.2 seconds

Sniper

• The Cozy Camper
  • heals +2 hp per 2 seconds

Spy

• Conniver's Kunai
  • upon backstab, steals all hp from enemy

Misc

• Payload Objectives (Carts)
  • heals +10 hp per second
• Resupply Locker
  • instant full heal
• Health kits
  • small: heals 20.5% of max hp
  • medium: heals 50% of max hp
  • large: heals 100% of max hp