Why are there different video frame rates?
Steve asks, "Why did American's change Film rate from 25 to 29.97 frame rate per second?"
The real question is why did everyone else on the planet change the frame rate from the original NTSC standard of 30 or 60 frames per second, established in the U.S. during the 1940's. NTSC introduced the 29.97 fps when color television specifications were defined in the 1950's because they needed room for the color data while broadcasting. The newer PAL standard you refer to was created by Germany in the 1960's with frame rates of either 25 or 50 fps.
The PAL standard, while very similar to NTSC offers a number of improvements over NTSC, primarily because the people who designed PAL had the advantage of understanding the limitations of NTSC. PAL builds on NTSC shortcomings with improved color and more lines of resolution. The 25 fps of PAL is mathematically easier to deal with for a variety of reasons, although the 50Hz refresh rate of PAL is certainly more visible to the naked eye.
Hopefully as we move toward a fully digital television experience, all of this will just go away and we can have something approximating a global television standard. Already we are seeing many of the high end HD cameras recording at 24 frames per second, which creates a new set of challenges to match up video with the limitations of both PAL and NTSC, while more closely approximating film.
In the meantime, unless you are trying to convert a PAL format video for playback on an NTSC screen, you typically don't need to concern yourself with either one.