Make your reservations up to 13 months in advance for above stated. They book up very far in advance and have a limited number of spots available. The mule rides have weight limits and other restrictions, so be aware of these. When we hiked the GC I wondered how the mules could navigate the trails and how fast. They are unbelievable at going up/down at a quite fast pace and look to do it very easily. They have never lost a rider on a mule in the Grand Canyon. They train the mules by carrying loads of supplies first, then graduate to carrying customers. When they built the bridges that cross the Colorado, they carried all the supplies down by mule! Even the long main cables were stretched across many many mules in a continuous strand. I have read that they practiced this feat before the actual trip down.
Fondest memory: Just being able to say "I hiked to the bottom of the GC and back out" does it for me. My wife and I did this in September 2002 and am planning another for May 2008.
For those of you who are feeling brave, you can go on a mule in a group and make your way down to the bottom of the Canyon.
Fondest memory: Thinking how glad i was about talking myself out of going on those mules. ;-)