I've noticed it myself twice. In the morning I bring up Mail and read what's come in overnight. Then a little later I re-open Apple Mail and the same messages download again. Of course my POP account is set to delete everything from the server, and my settings have not changed.
This is the first really bad behavior I've seen from Apple Mail since OS X came out in 2001. This most recent glitch seems to have popped up in the 10.6.1 update. There are enough people reporting it that it seems like there is an issue for some users, but obviously not everyone is seeing it.
There have been some suggestions posted, but while they worked for some they did not work for all. Are you seeing this strange behavior? Did it start with 10.6.1? Let us know, and hopefully Apple will kick the code for the next update and put this bad boy to rest.
Thanks to Mark for the tip.