Defining each one is a bit of a task w/o writing an essay. And being a mac person I can’t say too much for a couple of those formats. In my experience, mpg & mpeg are the same thing (although 1 might be mpg1/2, etc). MPeg stands for Moving Picture Experts Group. The major advantage of MPEG compared to other video and audio coding formats is that MPEG files are much smaller for the same quality. This is because MPEG uses very sophisticated compression techniques. Mpeg comes in 3 main flavours. MPeg 1, which is commonly used for the VCD format with a resolution of 352x280. MPeg 2 which is used for SVCD & DVD has a resolution of 480x480 for svcd up to generally 720x576/486 for dvd (was designed to support high resolution, high bitrate videos.) MPeg 4 is the newer one & still developing (there’s also 7 & 21.) The greater the mpeg version the more efficient the compression technique.

The Advanced Systems Format (ASF) "Advanced Streaming Format" is the file format used by Windows Media. Audio and/or Video content compressed with a wide variety of codecs can be stored in an ASF file and played back with the Windows Media Player (provided the appropriate codecs are installed). ASF is Microsoft's 'Streaming' format based around the MPEG 2 format. The quality is not as good as it's MPEG heritage suggests, but it does offer a much better file size to quality ratio. The CODEC had good specs on paper, but unfortunately, this CODEC can have serious synchronization problems on older PC's or even the newest Macintoshes, where the video and audio slide out of synch with each other.

AVI and Quicktime - are, strictly speaking NOT CODECs, they are simply file formats, a "shell" that contains other audio and video CODECs In the past the most common CODECs used with AVI and Quicktime were the Cinepak and Intel Indeo. I would recommend neither of these, as they're old, unsophisticated and do not offer very good quality or compression. AVI stands for Audio Video Interleave & defined by Microsoft.

DivX I know very little about, except it’s based on the mpeg 4 format. And it’s very popular. Has both high quality and low bitrate. They are usually only a fraction (around 15%) of the size of a standard DVD, even at 640x480 resolutions. They only take half the time to encode, and yet at the same time is smaller in size than MPeg 1. Quality ranges from net-streaming quality to DVD and better.

Keep in mind that quality of video depends on the original source material, the encoding settings, & quality (cheap/hq) of the codec used to encode. So whether you intend to encode/play back such material, the quality doesn’t ‘necessarily’ depend on the format. Some of these formats are more efficient at compression than others so a smaller file can result in equivalent quality.

I hope that’s of some help to you.