ALA New York Times. Although, I checked right before writing this, and it seems they got rid of it, or at least, they replaced it with a not less annoying, but potentially more profitable full page pop-up that forces you to sign up. I wonder if once singed, they have the auto-search. Can anyone confirm?
Those sites bug me too, as a heavy user of highlighting. It also causes me problems reading editable text, for instance in a text editor. Sometimes I'll accidentally click and drag a selection to a different part of the text without noticing. I usually notice, but if I don't it can cause problems later, especially with text that is code, where it can cause mysterious bugs to show up.
I don't highlight to read, and JIRA's new behavior irritates me. When I need to copy and paste something, having the box suddenly change to edit mode throws me off.