Serving up the low definition version of a video is a safe and sensible default for YouTube. But when watching videos on your desktop, hooked up via Ethernet to a speedy ADSL connection, it's a little annoying to have to constantly flick the quality up to 1080p or 720p.
To save your sanity, Chrome and Firefox both have extensions available that can remove this step for you, changing the quality as soon as you open the clip. For Google's browser, you'll want to hit up Auto HD on the Chrome Web Store. Auto HD also gives you the option to widen videos automatically.
Those using Firefox can install the YouTube High Definition addon. YHD lets you configure the browser to open videos in any resolution immediately and like Auto HD, in wide mode too.
It's a setting you'd think would be available in YouTube's user settings... and there sort of is -- you can make it so videos switch to their HD versions when you hit the fullscreen option -- but it's not the same thing. Fortunately, that's what extensions are for.