Universal and some early New Line DVDs usually do something like this... I just finished re-watching the original Final Destination and right after the still New Line logo, the blue MPAA R bumper shows up on the screen. When I was around 6, my reaction was this: "Why are they doing this? I ALREADY KNOW THAT IT'S A R-RATED MOVIE!"

Is there a logical reason behind this?

Not sure- when ratings started they put it at the very beginning, then they got moved to the end. VERY briefly in 2001, a few movies moved it back to the beginning, on a black screen with white lettering rather than blue and also showing the reason for the rating (I remember it being that way on Spy Kids, Get Over It, Crazy/Beautiful, Atlantis and Bridget Jones's Diary, all of which were distributed by Disney.) It's always annoyed me that most video editions cut them off, Universal was most consistent keeping them in.

Two movies, "Student Bodies" and "When Nature Calls" used the rating tags for comedic effect.

It is almost like they were stating:

"I'd you didn't figure it out, this was rated -rating- for these reasons... Thought you'd want to know"

Or maybe there was some requirement to have it included and they didn't ant to put it at the beginning. So they fulfilled the requirement even though it really didn't accomplish much else..

I never understood why they did it. The only reason a sane person would sit through the credits was if there was a scene there. Most normal people, especially when watching a dvd they owned, would have turned off the disc long before they got to the rating logo at the end of the credits.

I imagine this was just a requirement by the MPAA to cover any legal liability. It just didn't require them to place it at the beginning, so they placed it after the end credits.

Not every DVD or other video format shows the rating onscreen though- although the most recent ones tend to show it even before the main menu or when the movie starts, in some cases even making it unskippable which is annoying. Other countries seem to require ratings to be prominently shown on the front cover, which many have complained about.

It is shown at the beginning on later Universal DVDs and Sony/Columbia TriStar DVDs.