Are there any video codecs that are not compatible with the Raspberry Pi based on hardware requirements?
The video codecs actually fall into three categories - those supported and enabled by the GPU, those supported by the GPU but not enabled due to licensing restrictions, and those not supported at all.
As for details of what goes where, this blog post gives the info:
Two licensed codecs will be provided at launch, MPEG4 and h.264. Codec licences have quite an impact of the cost of the device which is why there are only two at this stage. There are non-licensed Codecs such at MPEG2, VC1 etc, but for the moment they will not be accelerated by the GPU.
Dom adds: As an aside, the GPU can hardware decode H264, MPEG1/2/4, VC1, AVS, MJPG at 1080p30. It can software (but still vector accelerated) decode VP6, VP7, VP8, RV, Theora, WMV9 at DVD resolutions. We are restricted due to licensing what we can support. We should be able to support VP8, MJPG and Theora, as I believe they are license free.
Update: License keys for MPEG2 and VC-1 can now be purchased on an individual basis from the store.