Yes, I know that there has been at least one similar thread before, but it's been pruned quite a while ago.Idea isn't really showing off every extension you have ever used, but the ones you find most useful. Maybe someone else will find an extension they truly like, because you said it was good.
Mine, in no particular order:
User Agent SwitcherMore of a web developer tool, but can be very useful with badly designed sites. I use it very rarely, but when I do it's almost invaluable.
AdblockDuh.
FxIFThis one is almost solely for photographers. It will display the EXIF-data of a picture
(provided that it has such data, of course), when you view its properties. It
is very handy, but mainly for select few people.
LinkyGives you an option of opening for example all image links
(or images) on this page to a new page. Or tab. Handy sometimes. Usually DownThemAll! is enough for my
pr0n picture gathering needs, but Linky can be handy in some special cases where DownThemAll! won't work with the page.
IETabBest thing ever. Gives you an option of opening pages in new tabs, using IE as rendering engine. Who needs IE now? Again, I don't need this often, but when I do... BTW, thanks to Aaron for finding this.
DownThemAll!Mass downloader. Most excellent for
pr0n picture retrieval. I use this very often. And no, that does not mean that I surf for pr0n all the time.
Tab Mix PlusI used to use Tabbrowser Extensions, but sadly it is so gifted in breaking the late Firefox versions, that I've switched to Tab Mix Plus. I don't remember anymore what the exact reason for using this was, but there's something missing in the regular tab system and this thing fixes it.
FasterFoxGives you a nice UI for the speed tweaks. You can do them without FasterFox, but it's much nicer with it. Just be careful, the most aggressive settings are not very nice towards servers.
LinkificationConverts text
(valid URLs, that is) into links you can click. This is very, very handy in forums that don't convert URLs automatically into links.
Leet KeyAgain an extension that I don't use too often, but it's worth its weight in gold when you need it. It can do lot of things, but I use it for deciphering ROT13-encryption. Very handy. 17 (4n m4k3 y0u v3ry |337, 700.
Proxy ButtonJust creates a toolbar button for quickly turning proxy on and off. It's worth to you depends very, very much on whether you need proxy for some sites and not for others.
SpellBoundIt's a spell checker. It's also the one extension I would keep, if I had to choose. Darned thing will even spell check live, while you type.
FoxClocksSmall but handy extensions that enables you to have clock(s) on the toolbar. Point being that they are always close to where you are looking (especially if you don't use task bar) and that it can have several. I have one showing local time, one GMT and one EST.
PDF DownloadOpening Adobe Reader documents in Firefox can be pain in the ass. And really slow. Slow, burning pain, that is. This thing fixes it by showing you a popup when you click PDF-link, with the option of downloading the darned thing (instead of opening it).
RefControlGet all sneaky and fool sites that check referrer. I use it forums where people post lots of stuff from Imageshack. No more yellow frogs.
VideoDownloaderDownload videos from several places. Like Google Video.
Night of Fire... StylishWith Stylish you can apply user styles to websites. Fixing badly designed sites, or make this forum look like it did a long time ago. For example. Using it effectively does require CSS skillz, though.
EditCSSNice CSS Editor for the sidebar. Good companion for Stylish - you can use EditCSS for tweaking the style and then apply it permanently with Stylish.
Then couple of good extensions that I
used to use:
phpBB User HideBasically a killfile for phpBB. Can make those pesky stoopid people disappear.
Doesn't work with SMF. Sucks.
BBCodeExtraIt's a handy context-menu thingy for adding some of the most often used BBCode-tags. Very handy with phpBB
(works better than the buttons in the posting screen), sadly not quite optimal for SMF.