Tests that don't test anything come in at least two categories for me:
- test that were useless, are still useless and will always be useless
- tests that are currently useless but were used in the "wtf should i write" phase of coding (templating/TDD/ whatever you want to call it).
I'm partial towards the seconds, and i like when they're not removed, because often you understand how the API/algorithm was coded thanks to them (and its often unit tests). But ideally, both should be out of a codebase.