I'd suggest using JW Player, a video player that supports even iPhone & iPad by using HTML5 video, and if the video format (like .mp4) is not supported by HTML5 video in your browser, it falls back to the Flash version of the video player.
MP4 H.264 will probably be the best choice, the format is supported by iPhone & iPad, and it plays in all browsers using the Flash version of JW Player.
You can download [skins for JW Player or you can [URL="http://www.longtailvideo.com/support/jw-player/jw-player-for-flash-v5/14/building-skins"]create your own skin](http://www.longtailvideo.com/addons/skins).
Thanks for the reply.
I was actually more referring to "creating" my own audio/video player, not using an API to redesign a player etc.
Yes it is possible, in much the same way that it's possible to design and build your own car. There do tend to be many compatibility problems that you will face, but yes it is possible to create your own audio/video player.
If you want it to work on a wide range of devices with a wide range of file types, you will be best served to stand on the shoulders of giants and use a pre-existing API, because they have already faced all of the compatibility problems out there and found suitable solutions to deal with them.