I generally agree with Jessica's answer. However, there are situations where they do not mean the same thing. For example: Shall I do this for you? Will I do this for you? These actually mean different things and in interrogatives, the two often mean different things. Shall I do this for you? means, Do you want me to do this for you, if you do want that, I will do it. Will I do this for you? means, It is clear that you want me to do this for you, but there is a question in my mind as to whether I will do it or not.

They mean the same thing. In the US we use will, shall sounds more formal or old. In England they are used interchangeably but shall is more polite and usually reserved for the first person. I shall get to this tomorrow, you will get to this tomorrow. Will is more common and it is never incorrect to use will anywhere shall is used. They both express the future tense.

If you are smoking a pipe and wearing a monocle, then you should use shall. Otherwise, you'll just sound silly. Example: Shall we adjourn to the parlour? (oh, and a slightly British accent helps too)