1) Learning the algorithms. I agree with the general criticism that these algorithms aren't that broadly applicable. I work on data storage software, so we use a few relatively fancy data structures, but even so most of my day to day work isn't on the code that manipulates them. That said, I think succeeding at these contests (especially when they're timed) requires you to practice avoiding bugs, particularly off-by-one errors, and I think that practice is pretty broadly applicable.
2) Thinking in terms of data structures. The data structures that a program uses are a lot more important than the actual code. Some critics complain that programming contests teach you to write messy code. I think that the people who are really good at programing contests who write messy code (ime, it's more compact than messy) do it because they've trained themselves to look at a program and see the data structures rather than the code, and in my opinion that's a better way to think about a program.
3) Learning to get good at something in general. This is the main reward I feel like I've gotten from these contests. I think many skills in life (including job performance and career advancement) can be developed the same way: study the rules, study the best competitors to understand what's achievable and what techniques are available, make an attempt, try to understand the results you got, try to improve your approach, repeat. I think programming contests are a great place to learn to do this (among many others, of course).