I normally use OpenOffice.org Writer in conjunction with the standard, soffice and Ubuntu dictionaries that come as standard with OOo Writer and Ubuntu linux.
Spotting this topic made me look at grammar checkers, and I know that AbiWord has an associated grammar checker of reasonable repute, although I haven't been able to get it working under Ubuntu yet. AbiWord could well be of interest to multilingual writers because it has many useful tools including access to online translators like the Google one from within AbiWord itself.
I was also inspired to add the LanguageTool open source language checker, from
http://www.languagetool.org/ , to OOo Writer. It seems to provide primitive grammar checking in a variety of languages and actually spotted a common mistake many native English writers make - the replacement of 'lose' with 'loose', so it can pick up words that have a legitimate spelling but are out of context,
Unfortunately it doesn't pick up all common grammatical errors
Both OOoWriter and AbiWord are multiplatform and are available for Linux and Windows