Your hardware (Projector, DVD player, VCR etc) will be designed to project a rectangular image so the software is the least of your worries if you are after a true circular image.
More likely you're after a rectangular image with a circular section (your images) inside a black rectangle.
Virtually all video editing software is capable of this and there are a number of ways of doing this. A couple are:
1) Use a "cookie cutter" filter to mask out everything outside the circle
2) Use an overlay of a black rectangle with a circle cut out.
Basically, don't worry - it's not only possible, but simple too