Gelatin is made of collagen, mostly from the tendons, connective tissues, and bones of mammals. Powdered gelatin is the most familiar, but leaf gelatin is gaining popularity. Five sheets of leaf gelatin are equivalent to a tablespoon, or one packet, of powdered gelatin. To use it, soften the sheets in cold water for 1-2 min before adding them to whatever liquid you're cooking them in, then heating that liquid until the gelatin melts.
Agar-agar is the vegan (and pareve) alternative, made from algae. Powered agar is usually designed to replace gelatin one-for-one, but in most cases you'll need to use more flake or bar agar than gelatin.
There's also isinglass (not to be confused with muscovite, a kind of mica that's also called isinglass but isn't edible). Isinglass is a kind of gelatin made from fish swim bladders and is used primarily in brewing.
More links:
Some health aspects of agar-agar
More about isinglass
