Just lost half an hour that I really didn't have to this issue, so I thought I'd post the solution here to save others from having to sift through hundreds of Adobe forum messages to find it.
AME was working fine last night and this morning, then suddenly refused to run. Here's what fixed it -
If you are on XP, delete this folder:
Documents and Settings\%username%\Application Data\Adobe\Adobe Media Encoder\4.0
If you are on Vista or Windows 7, delete this folder:
Users\%username%\AppData\Roaming\Adobe\Adobe Media Encoder\4.0
You should be able to launch now.
I was leery of deleting folders, so I just renamed it, but it still worked and AME just recreated the folder anyway.