Back to the topic at hand.
I cannot speak to the "most embarrassing" losses.  Embarrassing to who?  The players? The fans?  I guess I have never personally felt "embarrassed" by the outcome of a sporting event in which I was not a participant.  I will say that when I was a junior in high school, my 1600 meter relay team got lapped - that WAS embarrasing!
I can only speak to the most disappointed I've been in the team's performance during my 10 years as a season ticket holder:
2.  Michigan - 2003.  Oh, what could've been.
5.  Wisconsin - 2005.  We HAD IT WON
Anyway, that is my list.