I had this problem as well. After a while, it got progressively worse until it was sending me back to the home screen after just a minute or so of using just about any application. Same symptoms as others here: music would stop, black screen, then back to the home screen. I tried doing the reset function on the phone but that didn't help.
I finally did a Restore from iTunes do see if it would fix the problem. It did, but it also erased all my system settings so I had to set up all my prefs again. Since then the phone has been behaving better, but I have noticed it still crashing a few times, especially in Safari and Google Maps.
I really hope this gets fixed soon as it is my main gripe with the phone