I have been using WordPress for several years, but have yet to see a reason to employ tags over categories or tags with categories.
What is the thinking behind the two, and when are each appropriate?
Aside from the technical aspects, Categories are for broad topics while Tags are for adding more detail to your posts’ subject.
Lorelle has written the definitive guide on the difference between categories and tags.
You might also want to check out the WordPress.com guide on Categories vs. Tags.