I have a Debian media server which seems to be crashing several times daily for no apparent reason at all. It simply freezes up, without restarting, until you manually restart it. I have uploaded the syslog here and the kern.log here Any restart indications in the log file were done manually by me and not as a direct result of the crash.
I don't see any explicit question here, but here's what I would do to start debugging this issue.
The first thing I do in cases like this is to run memtest86 or memtest86+ a few hours on the machine. This will rule out a lot of the common hardware errors.
If that passes, I run mprime for good measure. It will check that the CPU continues to calculate most things correctly under stress. I've had subtle errors after several hours running this, although I have not had to use it in a couple of years.
Now, if these tests passes, your hardware and cooling should be fine. After this I'd try running the system from a live CD if possible, perhaps trying an i386 version instead of amd64, to see if there's something wrong there.
If this does not give any insight, feel free to update the question with any new information!