Knitted Casting On
Also called Knitting on. One of the easier casting on methods in knitting, the knitted cast on is useful to learn because it uses the same movements as knitting a stitch. It's a good casting on method for the beginner knitter. I've seen this referred to as a lace cast on, I guess because it makes a light, open edge, appropriate for lacy knitting. Knitty.com has a nice article including this method. Or if you prefer, this how to cast on knitting video from knitTV is great for beginners.
Cable Cast On
Very similar to the knitted cast on in how it's done, this method of casting on makes a firm, elastic edge, really good for the edge of sweaters and hats. I found a nice illustration of the Cable Cast On in the knitting book The Sweater Workshop.
Long Tail Cast On
Another popular cast on method, also known as the Double Cast On, Continental Cast On. I find this requires more dexterity than the knitted cast on, because the knitter holds two strands of yarn in their left hand and a needle in their left, so might be awkward for the beginner. But that might be because I knit English style (I hold the yarn in my right hand). Knittinghelp.com has excellent videos and instructions on the Long Tail Cast On.
Thumb Cast On
A very simple method, with some limitations. The edge it makes is not the prettiest, and the stitches can be tight. But good for beginners, and for adding stitches at the end of a row. Here is a good explanation of the thumb cast on at Dummies.com.
There are some other more specialized types of casting on in knitting, which are used for specific purposes. Beginners, don't worry about learning these, but you might see these in pattern instructions. Go to Cool Tricks in Casting On for information on Provisional Cast On, I-Cord Cast On, Tubular Cast On, Judy's Magic Cast On, and German Cast On.