I see Linux developers talk about regression tests but couldn't find where is the central repository of this (is there one?) Regression tests IMHO should be distributed with the source code so everybody can run them. (I understand testing a kernel is not like testing any other user space program.) The BSDs do it, for example.
I remember reading about a study about a very different style of development from years ago, where automated testing was NEVER done, but instead formalized models of the program were created and mathematically verified.
If I remember correctly, the final result was a similar level of quality to an extensively tested system developed today, and the code tended to be of somewhat higher quality thanks to the extra thought put into it. (But I'm only going off vague memories here... I might be misremembering)
I'm actually quite disappointed to see my original comment with a negative score. I'm going to assume it was just badly phrased, as I don't seriously think that anyone believes that more testing of software results in a decrease in quality.
I've seen projects with more tests than code, and I think that shows a problem with development methodologies. Simply reasoning about the flow through the code (and possibly using a powerful type system [think Ocaml] to help catch errors at compile time) would remove the need for many of these tests (not all tests should go, of course) and would result in tighter code.
I do think having a suite of repeatable test cases you can run against developing software is a useful thing to have, though. Not only can you test for correctness, but you can also run benchmarks against each modification to see if your performance or memory usage is going up or down.
It probably depends on what you're trying to do...