Video Editing - Adding Animation Clips

when you say add animation what do you mean?
on top? so that both are visible at one time? or alternating from one to another?

both are video right?
or you need the audio off of one and match with the video of the other?

I like a simple program called showbiz that might be able to do some of what you ask but I cannot be sure.
how large are your files?

Well, the animation clips that I would like to add are like the ones that are found in MS Office, with the file extenstion .gif

When I say on top, I guess I mean like how you put it, "both are visible at one time".

The file size is like 3 MB.

Windows Movie Maker II can do this, if your video file is not real big. However, it tends to stretch some gifs. I think you can put the files on top of one another to get the effect your looking for.
I once made a 15 minute video of just animated gifs, that turned out pretty good. Vegas Video can also do this and much more.