The bard is somewhat of a healer class, and he is not a cleric (although his primary function is not to heal, he's still a "support class")... I have to admit that i was a little baffled when i saw that the bard could cast healing spells...
The druid is a "nature cleric", and he can heal...
The paladin and the ranger can both cast healing spells, although they'll never be really good at it...
There are actually quite a few non-cleric classes that can heal..
Other than that... I'f you're talking about an alchemist, do you mean someone who can make potions? If you are, then, anyone with a spell list and the Brew Potion feat can can make potions. Of course, only characters that can cast healing spells can make healing potions...
You could devise a Prestige Class that allows you to copy potions, but we're stepping into House Rule territory now...
Other than that, you could invent a class that cures people the "normal" way, ie somewhat of a medical doctor, that uses drugs and plants and stuff to heal the sick and the wounded, but it could never, in my opinion, be as powerful as a cleric...
My 2 cents
Maitre D