What is the preferred file format for recording movies from a digital camera to be played back on a computer, uploaded to fb etc.?

My cameras have always been Canon, but lately they have switched to .mov, which I believe has limitations. I know I can either download a program to convert (I prefer to not have to do that) or I can switch to another camera brand.

So, regarding movie file formats, can anyone tell me which one will not give me a lot of headaches when it comes to sharing...mov, Avi, mpeg?