I was quite impressed by the spellchecking features of Konqueror - the KDE web browser. It highlights misspelled words as you type in web forms. Luckily, there is an extension for Firefox, which gives you similar functionality. SpellBound works for Windows and Linux builds of Firefox. Multiple languages, including English, Russian, German and so on are supported. The version, found on the main site, actually doesn't support on the fly spellchecking, but if you download the latest development version, it will do it happily. More information can be found here.
Note for Unix users: when you install the dictionaries, you need to have write access for $MOZILLA_HOME/components/myspell, which usually means being root. Don't trust the messages dictionary XPI shows during installation under normal user account - they are misleading.