An important part of my job is to analyze requirements and write specifications. I have found the technique of storyboarding to be extremely effective. A storyboard is a concrete rendition of a particular scenario - could be a use case or an XP story (see Martin Fowler on UseCasesAndStories for an explanation of the difference). Not only are storyboards great for sorting out requirements, they are also effective in communicating what needs to be built to developers, and as a starting point for the development of tests.
If what you are building is exposed to the user through UI, then the most likely form of your storyboard is a click-through of the UI. If what you are building is infrastructure, say an API, then your storyboard might be a click-through of the experience a developer goes through in authoring code that uses the API, or it might be a filmstrip - a series of object diagrams that illustrate what happens to the state of the system as methods are executed.
Tools that I have found to be particularly effective in developing storyboards, especially those that click-through a UI experience, are Powerpoint and Visio. You can really bring storyboards alive in Powerpoint using a combination of moving through slides, using its custom animation capabilities, and by mixing and matching graphics from multiple sources. And the Windows XP template in Visio is pretty useful too. I've put up an article with specific hints and tips on using Powerpoint and Visio for this purpose.
Interestingly, I soon move from sketching a storyboard on paper or the whiteboard to committing it to Powerpoint, as the latter imposes a discipline that forces you to make decisions and care about the detail. It's so easy to continue hand-waiving and putting off those hard decisions at the whiteboard. I don't spend a large amount of time getting the UI 'just so'. It just needs to be good enough to tease out those important decisions about what the requirements actually are.
If anyone has suggestions for alternative tools that could be used for this purpose, then please add them as comments to this post.