For misc file times .gz, .zip, and .tar are pretty much the standard. I don't know of any others other than Winrar or .sit compression, but those are OS specific. All operating systems have native extractors for the three that I mentioned and .zip is pretty much the business standard. What is the file extension that are on the compressed files?

If you mean audio/video compression then the answer is that most are just legacy compression systems. H.264 video is the defacto standard in video. AAC is the best in audio compression and very widely used however MP3 came around at the right time so even though it only gets about half the compression, devices still use it.