A simple example is an image-cropping system. The user has to click and drag. If you don't disable the selection and the user clicks in just a slightly wrong way they can end up selecting or dragging the image, which looks totally wrong for someone who wanted to select a region of an image. Both actions have the same user input (click, drag, release) but your intent is that it have a very different behavior than the browser default.

I travel a lot and have to use UIs in several languages, and being able to copy the text on button labels (or graphs!) to paste it into a dictionary is very important to me. On some sites I have to fall back to using the web inspector and it's just as annoying every time.

I disagree completely.

For the Github example, you want to disable selecting the file list header and, bizarrely, you tend towards disabling selecting the file list itself. Considering the files and their meta information are Github's content, disabling copy-pasting file names and commit messages is incomprehensible to me -- that's the last thing I'd consider disabling. And if I want to copy/paste the entire file list, I might want to copy the list header along with it for the benefit of the recipient. I wouldn't disable the selection on anything on your Github example.

The graph label example is just as strange. I tried the linked Morris.js example, and I can't select the label text. How is that a better user experience? What if I want to IM a friend the 2011 Q3 numbers? What if I want to search for similar data? Both quintessential web actions.

I think braking selection is almost as bad as breaking the back key, the cardinal sin of web apps.