Adobe wants people to use Flash to play videos, primarily because they own the technology behind it (which makes them lots of money), and have enjoyed the majority of video on the web being played via Flash for quite some time. Adobe, by virtue of owning Flash, is the only real player in the Flash playing and video encoding game. They want Flash on every device in the world, so they can sell their tools to author Flash. Adobe as a company [still makes most of their money on selling people tools][adobesales] to make things with. Adobe has spent a lot of money making Flash and their Flash editing tools.
[adobesales]: http://www.businessinsider.com/chart-of-the-day-adobe-revenue-2010-5 “Adobe Revenue 2010”
Apple wants people to use H.264 to play videos, primarily because their mobile devices (which make them a ton of money) can decode the video stream in hardware which is [a big win in battery life][battery] .vs. decoding in software like Flash. Apple controls the decoding of H.264 on the Mac and iPhone/iPad lines, so they don’t have to wait for anyone else when they want to do something new with it. Apple has spent a lot of money and time making H.264 work great on their devices.
[battery]: http://www.anandtech.com/show/2834 “Battery Life”
Google just wants people to play videos. They’d prefer it if the technology used to encode and playback those videos didn’t belong to anyone, so they don’t have to deal with the politics of being nice to some other company because they need their support vis-a-vis video. They [bought a company called On2][bought] and [open sourced a video codec and container format][webm] (which may have [some severe patent problems][tech]) to accomplish this end and try to diffuse the situation. Google is the only company in this tug-o-war who actually makes money selling videos, or more precisely, renting the eyeballs of people who are viewing videos to advertisers.
Due to the above, video on the web is a nightmare right now. There is no video format you can encode to that will play in the big three: Safari, Firefox, Internet Explorer, unless you want to use Flash to play the video. Which means users will need to have Flash installed on their device, in which case it will not play on the largest mobile device market: the iPhone, iPod Touch, and iPad, or even current releases of the smaller ones, like Android, which also do not support Flash. If you encode to H.264, it won’t play in Firefox or the current version of Internet Explorer (8), but will work in Safari, Chrome (on the Mac), and the upcoming version of Internet Explorer (9). Adobe has pledged to support WebM in it’s Flash products.
There is no way Apple is going to support WebM for their mobile platform unless it can be decoded in hardware. Broadcomm, a major producer of chips for mobile device, [has announced a chip which will decode VP8 in hardware][broadcom], but this is fairly new development. It is not unreasonable to consider that Apple has plenty of so-called “skunkworks” projects to play all kinds of Video content on iPhone and iPad, but it’s pretty unlikely that we’ll see any new video support in the upcoming new iPhone model.
[broadcom]: http://www.broadcom.com/press/release.php?id=s471536 “Broadcom Accelerates WebM Video on Mobile Phones”
[bought]: http://techcrunch.com/2009/08/05/google-acquires-video-compression-technology-company-on2-for-106-million/ “Google Buys On2”
[webm]: http://www.webmproject.org/ “WebM Project”
[tech]: http://x264dev.multimedia.cx/?p=377 “A Technical Analysis of VP8, the Codec used for WebM”