The last class I took was Bikram. It is for athletes or for people who are willing to sit out for part of the class while they catch their breath-lol, it's pretty intense! It is a type of "hot" yoga where the room temperature is up over 100, but the same exact routine is taught in every class. Class is long-1.5 hours. You will sweat profusely. PROFUSELY. I could actually hear sweat dropping from the shorts of the guy in front of me, and it was pretty gnarly. Pros: It's an AWESOME workout. Members tend to motivate and support each other. It's probably unlike any workout you've ever done before.
Cons: some of the Bikram instructors are militant. FOr instance, some of them only let you drink your water in between certain poses. I once got scolded for taking a sip at the wrong time. They like you to keep your eyes open at all times (sometimes I like to close my eyes when I stretch-got scolded for that too!) They are nit-picky about form as well, but if you're a newbie they will cut you some slack.
In my home I occasionally do Vinyasa, preferably to a Rodney Yee DVD. I like Vinyasa because you just move from one pose to the next, to the next, without holding the pose for an extended period of time. You hold each one for maybe 4 breaths. All that movement provides a gentle aerobic workout and you become familiar with a lot of different poses and series. ONce you learn a particular series of flowing poses you can do them on your own without the DVD, wherever you want. I believe Ashtanga and Power yoga are the same as vinyasa, but I could be wrong.
In college I tried Hatha Yoga. If I remember correctly the focus was more on holding poses, achieving the best possible form, etc. I found it to be boring, but many people love it.
Hopefully that was helpful