Same thing!!
I am having the same issue! Its not about using other peoples accounts either. None of these emails addresses popping up are any that I recognize. I counted 15 different Apple ID's its asking me for the password. I've sent emails to all the people tonight, no replies yet.
When did it start happening on your iPhone? Mine started yesterday afternoon. I had my iPhone 4S syncing to my computer over WiFi and backing up to iCloud. I noticed something weird when I went to check my email after I woke my phone up. It was asking me if I wanted to download an app required for one of my bluetooth devices. I knew I had it installed, so I swiped to my next screen, and many of my folders and apps were missing over several screens.
I plugged it into iTunes and restored it. Then I had it restore my backup via iCloud. Once that was finished, everything looked fine. It wasn't until I started updating my apps, that it was asking for random Apple ID passwords. 15 total that I had to click Cancel on. It ended up updating all of my apps anyway, all under my account. I thought that would be the end of it.
I can replicate the issue if restart my phone and run updates. I get the same 15 Apple ID's.
I would be interested to know if any of the ones you are getting are the same as mine. They are all yahoo, hotmail, msn, live, and one other. Also see if you can replicate the issue by trying to update again.
This is really weird that no one else is reporting this issue. I have been looking on twitter to see if it happening to anyone else. Its gotta be something with iOS5, because this never happened before, but then again, it could be iCloud too.