The Mozilla Suite and Mozilla Thunderbird have had a built-in spellchecker for a little while now. And someone came up with the idea of using the spellchecker for with form fields (input boxes and textareas). But, for the most part, the feature request languished.
However, a guy named Torisugari has come up with a workable setup (for both Mozilla Firebird and Mozilla Suite). As mentioned in the Firebird forums, he’s created an XPI browser extension that makes use of the existing spellchecker libraries adds a spellcheck option to context menus for input fields and textareas.
The links to download are included in Torisugari’s forum posts and, if this feature interests you, I’d recommend reading the whole thread (or at least skipping to the end) since the later posts point to more recent versions of the extension.
And, as a bonus for Torisugari, he may end up with some money from this — there's a SourceSupport bounty for adding this feature (SourceSupport is a site where users can pledge towards feature requests and new software). It currently stands at $42.84 and I’m tempted to chip in myself.