1) High-frequency trading. Very programming oriented as trade latency is everything. You'll need to be really good at making C/C++ code really fast. Math is somewhat less important than other fields.
2) Derivatives pricing. Usually working for banks/hedge funds, and use various methods (Monte Carlo, PDE, transform) to price options. Will need to know C/C++ and/or probably Matlab, C# (Excel is king here, so MSFT languages is a big deal), and Python is on the up and up. Will need to have a serious math background. This is more or less what I do.
3) Algo trading. Uses mathematical techniques to find patterns and execute trades. Probably works for a hedge fund. Programming languages vary by fund and include Matlab, Python, C/C++, Java (one uses Ocaml). Less theoretical, lots of playing around with data.
4) Quant risk. Usually works for a bank or hedge fund in the risk department. Responsible for things like building VaR models. Usually requires light programming (VBA, although serious languages help), and some lightweight math.