Burn a memtest86+ cd/floppy and let it run till it goes through all tests.
http://www.memtest.org/
If it reports errors, you know you have a bad memory problem.
If it reports nothing there... then check your swap partition for errors?
grep swap /etc/fstab
/dev/sda2 swap swap defaults 0 0
swapoff /dev/sda2 (or whatever your actual swap partition/s are)
mkswap -c /dev/sda2
swapon -a
That of course assumes your system isnt swapping heavily and has enough memory to function without a swap partition.
Doing the swap test can be done on a running system...
Doing the memtest test would require taking down the system and having console access to it to watch the output.
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