Is there a Firefox add-on to use vim to edit textboxes?

Vimperator makes Firefox act very much like VIM:

Vimperator is a free browser add-on for Firefox, which makes it look and behave like the Vim text editor. It has similar key bindings, and you could call it a modal web browser, as key bindings differ according to which mode you are in.

Once you have the cursor in a text box, hit Ctrl-I to open in your editor, which defaults to gvim.

It's All Text!

From the extension page:

At the bottom right corner of any edit box, a little edit button will appear. Click it. If this is the first time you've used "It's All Text!" then you will be asked to set your preferences, most importantly the editor.

The web page will pop up in your selected editor. When you save it, it'll refresh in the web page. Wait for the magic yellow glow that means that the radiation has taken effect!

The current answers don't work anymore now that Mozilla removed XUL in favour of WebExtensions. With recent firefox versions, there are the following options (sorted in descending order by the current popularity on addons.mozilla.org).

GhostText provides instant synchronization between editor and textbox via editor-specific plugins. The project is on github and the vim extension is written in Tcl.

withExEditor is cross-platform but requires a native application written in node.js. In addition to editing text fields it also allows viewing the source of the page, MathML, SVG and the current selection. The project on github and the native node.js application

Textern requires a (currently) Linux-only native application written in Python. Synchronizes the content of the text field while you type in the editor. The extension and the native app can be found on github

It's All Text! will let you use whatever editor you want. To use vim with it, you'll need a small shell script to open it in a terminal:

#!/bin/sh
exec xterm -e /usr/bin/vim "$@"

If you have GVim, you won't need the shell, script, obviously.