Nothing usually, like a skill check it cannot be critically failed because that does not make sense. If you want, I have used the following house rules (DND3.5):

~ Finish adding your initiative together:

~ Higher than something you are fighting (eg. and ooze), you go last for the first round and then in the normal spot for the rest.
~ Less than everything, miss the first round and then you go as normal.

However, I'm not a complete monster, it works in the other direction too.

If you get a score 10 or more higher than EVERYthing/EVERYyone else: 
~ You get an extra partial/swift/standard action for being just that aware/quick. 
~ *For rogues sneak attack does not apply because if they are going first you will get sneak attack on the creature anyway and I'm afraid of that many d6s. 

Thats my personal ruling, no real rule for it that I know of.