Thanks for the replies. Screensaver and power management were not enabled. I've checked the root partition with e2fsck -ccfkv; no disk errors.
It might have to do with doing things at 100% CPU. Thunar apparently occasionally crashes when that's true. (I didn't have conky before, but did notice (silent) crashes. Now that I have Conky that seems to be a criterium.)
You should check the logs in '/var/log/messages' and syslog.
I had a look. The things that jump out are "quirks" reported: my mobo uses some old vt82c686 chipset or something; and apparently wicd segfaulted once.
Should I remember the times of the crashes, or is there another way to search through those logs? :-/ Searching for "rsyslogd" seems to look up the start of the log (among other things).
BTW hopefully unrelated is that I get a kernel failure or something when I try to mount a cdrom (not auto-detected, blurts out "dunno what iso9660 is" if I try manually). Could it just be the old guy is going to kick the bucket soon? :-/ Maybe I should do a little stress testing in Windows, to exclude that...