You should strive to make your tests automated wherever its realistic to do so. Rails makes it easy to unit test your model and controller code, and has functional testing to test your apps end to end functionality too. Not testing your code properly is a form of professional malpractice IMO.
Untested code is pretty worthless, tests ensures that your code is behaving like it is specified, it allows your code for easy refactoring.
That's the big one for me. It's usually pretty obvious when your code is or isn't working during the initial development. But when you come back to it a month later to make a change, it's so nice to have "rake test" waiting to flag everything that just got broken.
-- James