I may be the only person in the world who'd have a use for this (which I'll explain in a minute), but if not I think it would be really cool if someone made it:
I'd like an extension or other clickable doodad which allows me to randomly re-order all open tabs in a Chrome browser window.
Every day at Rational Review News Digest, I select and post excerpts of (and links to) numerous political commentaries.
At the end of the day I select a "top five most interesting" (from those I've found and those added by other editors) to head up the email edition, but in general I try to "mix up" the order in which I post them -- that way if the Cato Institute's latest piece (ferinstance) is at the bottom one day, maybe it's near the top, or in the middle, the next day.
I used to do that by searching sources in various orders, but these days I just run through my bookmarks, go to random.org, and start adding stories in the order I get from "rolling the dice" there.
It would be nice to be able to jumble up the tab order with a click or two.
Honestly, though, I can't think of a great number of other uses for such a thing, so I guess I'll have to do without it, or learn how to code it myself.