Apparently there's a "Mars Curse," namely just that a high percentage of missions to Mars have failed: 19 of 39 Earth-to-Mars missions have failed. NASA's gone 13 for 18, so the percentage for everyone else is actually much more dismal: out of 21 missions by others, only 7 have succeeded.
Wikipedia's Exploration of Mars
page has a list of mankind's missions to Mars, and I found three failures in particular that were interesting--two of them by NASA, even!
- Viking 1 Lander
The Viking 1 lander lasted longer than the other three components of the Viking project (the other lander and their two orbiters), and was still going pretty strong on the Martian surface until software uploaded to it in 1982 overwrote the program in charge of aiming its antenna, causing permanent loss of contact with the lander. Who knows what it's up to now? (Well okay its radioisotope power probably ran out.)
- Phobos 2
So funky that they gave it that triumvirate control scheme (and there's the notorious Soviet penchant for redundancy again ;)! I'd like to know more about it, because if the computers were identical, you'd think they would have always given the same responses.
- Mars Climate Orbiter
This probe burned up in the Martian atmosphere after going too low; the error was due to the thruster control software making calculations that assumed the numbers it was given representing the Imperial system (pounds force), while as far as the hardware configuration went, they were supposed to be metric (newtons)--so the control program overcalculated how much thrust to apply by a factor of 4.45:1, the conversion ratio between newtons and pounds force. Oops!