I previously mentioned some problems I was having with my phone. If you read the update I wrote at the end, you will see that I traced the problem to a phone case I have which has a magnet in it. The phone has absolutely not locked up since I stopped using that case. The only thing I can trace the phone problems to is the magnets which hold the flap shut.
I have read pages that talk about how AT&T employees are telling customers to not use cases with magnets. Some of the reasons are bizarre and totally impossible. Such as the magnets messing up the video or erasing the hard drive. There is no traditional hard drive in an iPhone. Magnets will effect a CRT monitor but not an LCD. I think these are reasons made up by the individual employee to explain why not to use a magnet in the iPhone cases.
I have also read where people have said there is no way a magnet could negatively affect the phone. There were some reports of problems, while not the same problem as mine, which are consistent when magnets are involved. I can verify that the magnet is definitely the culprit of my phone locking up.
All that to say, while there is inconsistent data, it does appear that magnets can affect the phone negatively. How strong of a magnet? What will the symptoms be? How long of exposure to the magnet? Those are questions I cannot answer. But I can say that if you are having problems with your iPhone and you have a case with magnets, then try some testing to see if the case is indeed the problem.