What is the python "with" statement designed for?

I came across the Python with statement for the first time today. I've been using Python lightly for several months and didn't even know of its existence! Given its somewhat obscure status, I thought it would be worth asking:

1. What is the Python with statement designed to be used for?
2. What do you use it for?
3. Are there any gotchas I need to be aware of, or common anti-patterns associated with its use? Any cases where it is better use try..finally than with?
4. Why isn't it used more widely?
5. Which standard library classes are compatible with it?