Firefox has a built-in spell checker, but by default it only works on text fields of more than one line. However, you can make it spellcheck all fields with the following steps:

1. Start up Firefox.
2. Type “about:config” into the address bar in Firefox and hit enter.
3. Click “I’ll be careful, I promise!” (if the warning appears).
4. Type “layout.spellcheckDefault” into the Filter field.
5. Change the value for the layout.spellcheckDefault field to “2″ instead of “1″ (default).
6. Restart Firefox and you should be set.

If you are new to about:config in Firefox, checkout MozillaZine’s intro.