Healing has been pretty interesting through the different editions of D&D. I wrote
an article about it recently, but here's a few extra notes:
The cleric in AD&D begins pretty much equivalent to a fighter. They also have a few healing spells. As they gain levels, they become less effective fighters (compared to the fighter), but more effective spell-casters, though never to the offensive power of magic-users. Healing for the first six levels is actually an extremely minor component of the class. A sixth level cleric with a decent wisdom can, if he puts all his first level slots into cure light wounds, cure 5d8 hit points per day. Even once they gain 4th and 5th level spells, they don't have the spell slots to really do much healing.
Supplements to AD&D 2E made healing more effective, and 3E made it more effective yet. In 3E/PF, you didn't really need a cleric for basic healing, so many classes can do it.
The trouble is in 3E/PF is that there are forms of damage that only* clerics can heal. Ability drain and level loss, in particular. You need the full restoration spell, and there are a significant number of creatures that inflict that sort of damage, especially in certain adventure paths. Classes that look like they could replace the cleric, such as bards and druids, can't deal this. (* In the core 3E books, only the cleric gains
restoration at a decent level; the paladin gains it very late. There are a very few classes in 3.5E supplements that can cast it. There are a few more in PF).
Do you actually need healing? Well, not if you're playing a campaign where you can go back to home base and avail yourselves of clerics (or just rest for a week or two). You'll be fine. However, if you're in the middle of a big adventure path or similar where there are (a) time constraints or (b) location constraints you're going to need a healer. Try
Descent into the Depths of the Earth without a cleric. Go on...
Cheers!