Yes, I remember trying to use Google Books Ngram Dataset [1], but it was too tedious for me to setup and maintain a server with the data for a purpose of a quick-and-dirty tool (that's why I asked for a ready API). Still, using it is probably a nice idea for a more ambitious side project or even a startup.
EDIT. Actually I would happily pay for a tool that implements the idea. Grammarly has paid plans but $30/month is too steep (for my types of usages), and the types of grammar checks it performs is not exactly what I need (which is what real people in real situations use).
LanguageTool has limited support for using Google's n-gram data to find spelling errors. It only uses 3-grams, and only for a list of commonly confused words. I'm not aware of any Free Software that does better.
EDIT. Actually I would happily pay for a tool that implements the idea. Grammarly has paid plans but $30/month is too steep (for my types of usages), and the types of grammar checks it performs is not exactly what I need (which is what real people in real situations use).
[1] http://storage.googleapis.com/books/ngrams/books/datasetsv2....