I use the BBC iPlayer. Every so often. It’s pretty good.
Only problem on my system is that the iPlayer does not like staying fullscreened on one monitor if I need to use the other screen (same issue with all other flash viewers it seems). Next best alternative is to view the video in the pop-out window; unfortunately, the window is rather small. Rather than try to fix the fullscreen issue, I found that adjusting the flash object dimensions manually did the trick. This does get rather tedious, but luckily, I have Greasemonkey installed.
Writing this was quite straightforward: this is a simple script which resizes the pop-out window to a nice size (HD-ready view of 1280×720), and allows you to resize the player by resizing the window (big criticism of the default behaviour).The bulk of the code is along these lines:
player.width = 1280;
player.height = 834; // 720 + 114px of iPlayer chrome
resizeToPlayer(player); //window.resizeTo(1286,916)
window.addEventListener('resize', function() { resizeToWindow(player); }, true);
Install Greasemonkey if not already (Firefox only), and install this script from the userscripts.org page.