I recently found the website freecrosswordpuzzles.com.au. It's a pretty old website, but it's got a heck of a lot of free crosswords on it.
However, the crossword interface lacks some keyboard navigation options. Unlike the New York Times crosswords, you can't press (shift) + tab/enter to move forward a clue (or backward) a clue. The lack of this feature made filling out the board a little painful.
On a whim, I whipped together a browser extension to add tab/enter key navigation to the site, and it works good enough. I made the icon for the extension using Hundred Rabbits' Dotgrid tool.
This was a nice little project I spent a few days on (coding + uploading it to Firefox/Chrome).