Here are some specialized methods for casting on in knitting. The more basic types of casting on are in the How to Cast On page.
Provisional Cast On
The provisional cast on is used when you want to use the cast on stitches later. For example, a scarf with a symmetrical design can be started at the center with a provisional cast on. You knit one half of the scarf, then slip your provisional cast on stitches back on to a needle, and knit the other half. Knittinghelp.com has an excellent instructional video on how to do a provisional cast on.
I-Cord Cast On
Tubular Cast On
I first saw this term in Reversible Knitting by Lynne Barr. In Barr's book, it's used for double-knitting and uses two colors of yarn. But it can also be used for a really stretchy edge, maybe for a single or double rib cuff. Check out Eunny Jang demonstrating a tubular cast on at knittingdaily.com. And here's another variation of the tubular cast on at fluffbuff.
Judy's Magic Cast On
I've never needed to use this, but I love the name. As far as I know, it's usually used for sock toes, but you could use it in other circular knitting where you want a seamless start to a closed tube, like amigurumi, for example. Here's the article by Judy Becker herself at knitty.com.
German Cast On
Also called German Twisted Cast On, Twisted Cast On, Norwegian Cast On. Again, another cast on I haven't needed (yet), which is also usually seen in sock knitting. Knitting on the Net has useful instructions.