I'm was having the same general issue with Sublime Text 3. It was all working fine earlier today, then suddenly all HTML documents have no syntax highlighting. When I set the syntax to HTML it shows HTML as checked in the selection list, but the active syntax in the bottom right of the editor shows up as PHP. (and no functioning syntax highlighting)
In my case PHP files also show up with PHP as the selected syntax highlighting, but syntax highlighting does not work.
I did notice that the AngularJS package adds "HTML (Angular.js)" as a syntax highlighting option, which when selected was working just fine. As I installed that package yesterday I thought it may be the culprit, but after uninstalling it the issue persisted. After re-installing the AngularJS package the "HTML (Angular.js)" syntax highlighting no-longer works, and PHP is shown as the active syntax in the bottom right of the editor.
Initially restarting Sublime did not appear to resolve this issue, but a recent restart of the application appears to have (at least temporarily) resolved the issue. I'm still posting this here just in case some of this information helps address this bug, which appears to have been around for a while.