I mostly used MySQL. But for my app, I now use CouchDB. It has its limitations, but the automatic sync between devices is pure gold. I haven't written a single line of sync code and it just works. It baffles me a bit that CouchDB isn't more popular and that people rather use MongoDB for NoSQL, which doesn't come with the same syncing capabilities.
Adding to this: if you want sync out of the box and like NoSQL (and your app isn’t super complicated), CouchDB is clearly better than Postgres (and Mongo of course).