The add-ons I always add to other people's computers after installing Firefox for them. Don't forget to install Flash, too, from http://get.adobe.com/flashplayer/.
Blocks annoying video ads on YouTube, Facebook ads, banners and much more.
Adblock Plus blocks all annoying ads, and supports websites by not blocking unobtrusive ads by default (configurable).
Collector's Note Makes websites much easier to read by removing distracting ads.
This add-on is a modified version of Tabs Open Relative (https://addons.mozilla.org/firefox/addon/1956) combined with dikrib's fix.
Tabs open to the right of the current one, external links open according to browser.link.open_external.
Collector's Note This enables a small but helpful behavior concerning opening tabs. It really should be built-in to Firefox.