What codecs will be supported with the HTML5 video tag?
Will it vary by browser, or is there a spec of specific codec that will be supported?
Originally, Ogg Theora video was the expected lowest common denominator. However, companies such as Nokia and Apple expressed concern over that format and the specification was changed to avoid listing a specific codec. This leaves us with three formats, none of which are fully supported in all major browsers.
Currently, the situation looks like this:
If you consider the current market share of each browser, the most common support is Ogg Theora and the least common is H.264, largely due to Ogg Theora not being encumbered by any known patents whereas H.264 is. Due to the costs behind H.264 support, Firefox will most likely never support H.264 and Opera has taken a similar stand. With Chrome now in the same boat, the only current browser that supports it is Safari. However, Ogg Theora is widely considered a mediocre format (its advantage being openness rather than the encoding itself), so VP8 support is growing as an alternative open/free format. So, for the time being at least, codec support varies. The most likely format to gain universal native support is VP8, but it's not going to happen in the near future.
Note that this covers only native support. For instance, it's possible to add H.264 support to Firefox 3.6+ with a plugin.
Other platforms of note: