I remember we had a thread on Firefox extensions on the old site, I'd like to restart it and ask what Firefox extensions people use and recommend.

Here's two recommendations to get things started:

IETab - There are several extensions to allow you to open pages in Internet Explorer, but none I've found are as good as this one. It incorporates the IE render into a tab in Firefox so you only have one window open and you can set up a list of sites to always render using IE (e.g. Windows Update).
http://ietab.mozdev.org/

GooglePreview - Adds a small screenshot to Google Search results of the website. More cosmetic than anything else, but I find it's slightly easier to recognise a site from the picture than the text.
https://addons.mozilla.org/en-US/firefox/addon/189