(1) An easy way to download YouTube videos (preferably, any site's videos, but YouTube is the obvious target). There used to be several extensions that did this, but they all seem to have been broken by some recent change Google made.
(2) An URL rewriter: something that lets me set up a list of regex-based transformations to apply to any link I click on, redirecting me to the transformed URL instead of the original one. There are all sorts of uses for this, but the one that keeps annoying me on a regular basis is sites like DeviantArt that make you go through an "are you sure you want to leave our wonderful site?" page on every outgoing link. (I seem to recall something like this existing for Firefox, but it's been a couple of years since I used Firefox regularly and I can't find anything like this in a quick search of their addons page.)