Four classes heal, and Forever gives each of them something new.
Priest: Blizzard calls it the most versatile healer, with shields, heals over time and direct heals. Discipline gets Penance and Holy gets Prayer of Mending. Several Priests can each keep their own Renew on a target.
Paladin: the strongest single-target healer in Blizzard's description. Holy Shock moves to 21 points with a 10-second cooldown, and Light's Vigil is the new capstone for group healing.
Shaman: Chain Heal plus Water Shield at 11 points and Riptide at 31. Saved totem sets cut the setup before every pull.
Druid: heals over time, now with Wild Growth. Revive at level 12 brings back a party member out of combat.
Easiest to level
Shadow Priests and Feral Druids level comfortably and switch to healing for dungeons, especially with dual spec from 40. Paladins heal well even as Retribution. Shamans are sturdy in mail.
Our pick
If you want to heal everything, a Priest. If you like keeping the tank alive above all, a Paladin. If you want to heal and still be useful in melee, a Shaman. See the class pages for what's new in each tree.