OK, maybe not indispensable. But I really don't want to be without these -- I use them constantly, and they spare me untold amounts of grief (and yes, obviously I use IE View all the time, but I'm talking about other people's extensions at the moment). I don't keep too many extensions installed for more than a day or two; but a few seem like part of the browser to me now.

spellbound - Spellchecker for Firefox 1.0 and the Mozilla Suite
Just started using this, but I'm very happy with it. Spell check any text box with a right-click. Great for checking, say, the title of this blog where I'd initially written "Indispensible"
Quickly add a blog entry regarding the current page, including any selected text. I use this to blog MP3s, etc. for later download; also great for linkblogs, etc. Very handy.
BugMeNot extension
Man, do I love this one. Land on a mandatory-registration page when trying to read a news article? Right-click, select BugMeNot... Automatically grabs information from the BugMeNot site, fills in the username/password fields, and submits the form. Didn't realize how badly I wanted it until I actually had it installed. The second thing I add to a new Firefox install (right after IE View).