If you're developing something which must work 100% every time or else someone will die, then unit tests are a must.
If you're developing with people who break the build all the time, then unit tests are useful.
Unit tests that aren't 100% up to date with the code are worse than no unit tests.
If any piece doesn't succeed, the command stops. No push without unit tests passing.
Unit tests are a safety mechanism- you can easily bog yourself down with too many, tying things up in bad ways, or presuming a specific design. But do you really want to live with no safety at all?
The art, as I see it, lies in writing tests in such a way that you get the guarantees you need, the safety of not letting the next guy (or yourself) screw it all up during later changes while simultaneously not preventing you from doing needed refactoring.
It's a fun challenge.
If any test fails, it is because you broke it just now, so you go in and see if your test is broken, or, as is often the case, your refactored code is breaking the expected behaviour of the tested code.
A bit of a tautology... broken code is broken. Unmaintained code, even unit tests, should be deleted.