MemTest86 and ...
[link|http://www.memtest86.com/|MemTest86] - I've not used it myself.
For the power supply, there are often other indications of problems. E.g. my old 486 would die during the initial BIOS message after painting random numbers of text characters of the message. Swapping the PS out fixed it.
The simplest way to check it is to swap in a new PS. If you don't have one to swap in, then you might get lucky by simply checking the +/-12V, +/-5V lines and seeing if they are in-spec. But usually when PSs die they have problems supplying enough current. It's more difficult to check that (you have to have an ammeter in series in the circuit).
HTH.
Cheers,
Scott.
