You can play ASFs and avis on macs with Windows Media Player for the mac and I think certain avis can be played with Quicktime. I know WMP for mac supports MSMPEG4v1 and MSMPEG4v2, and by now might have support for v3, v7, and v8 of the MS codecs. Also there is a divx codec out there.
You can play movs on Linux if the mov was encoded with a codec that your player supports, like cinepak. Currently there is no Sorenson video support though.