Wow this is such a simple question, with a rather complex answer! The short answer is: A LOT. You are going to get a different list depending on who you ask, so I'll give you my perspective. I won't be able to list all of the types of lawyers, but here's a starting point:
First I would split civil law and criminal law.* Civil law is where two people or companies are engaged in a legal discussion, whereas with criminal law the legal discussion entails an individual vs. the state. Lawyers rarely move between these fields and they're very different. Within criminal law, I think (although I never practiced it) the big division is white collar crime versus other crimes (robbert, etc.). Within civil law there are a ton of specialties. Some big ones: business law, IP/patent law, Antitrust law, Securities law, etc.
*Unfortunately, there are some legal specialties that do not fit neatly into the civil/criminal divide. This is where it gets messy. Immigration law and social security law are two examples.