You can do it with one of the hosted services. I don't know which ones support it exactly, but GoatCounter does (although it's kind of an undocumented feature until I merge PR #122).
Cool, I saw GoatCounter on HN a few days ago. I've looked into ways to get a user count without JS and without paying for hosting, but no luck yet. If you find out what free services support it I'd love to know.
But any service that sends something like "GET example.com/collect?path=/foo" can be loaded with an <img>. It's perhaps not an explicitly documented feature, but it will still work :-)