DivX is a compressor that conforms to MPEG-4 Part 2. XviD and some versions of Windows Media are also implementations of the standard. So anything that can decompress MPEG-4 Part 2 should be able to handle things compressed with DivX.
As for actual decompression libraries, I'd recommend libavcodec. It's widely-used (= good support), cross-platform, and open-source (LGPL, so can be used in commercial apps). It's also fairly easy to use from it's C binding. It can open and play many different codecs (and with libavformat, handle many different wrappers i.e. avi, mkv, etc.).
If it's Windows-only, using the OS-provided Video For Windows might be a better option if you just want to play MPEG since you wouldn't need to ship it with your app and you avoid potential license issues. Be warned, though, that this requires the user to have certain codecs installed. On Win7 (and Vista I think) the MPEG codecs required to play DivX/XviD are installed by default, however they're not on XP...