Dylan Smith writes about testing: Unit tests (automated, written by programmers, repeatable), Acceptance tests (stories or scripts that can be done by developers or users and test high level requirements) and Exploratory tests (noodling around by a clever person to see how an app is doing). I like these categories and I do all three on my projects. I think a lot of developers get excited (rightly) about Unit tests and run the risk of forgetting the other two. You still need to lead your users through a structured process that causes them to conclude you have finished their project. (And you still need to rehearse that structured process yourself so you know in advance it will pass.) You still need to play around with it a bit, outside of the confines of test cases, and assure yourself it really is a good application.
We're not TDD, so I don't write the tests and code to them. But I write the scripts for Acceptance testing as we develop stories and requirements. They're also a fine way to bring a new programmer up to speed on a project by leading them through what it does and how you know it's working.