Right now I am utilizing the (Jazz Plugin). This supports most major browsers on PC and Mac, and the author says he is working on versions for mobile platforms. But there is not yet a timeframe for release.
There is midi.js, but the documentation is a little sparse. Does this work on iPad? Android? Also, it takes a moment to load, which is inconvenient for those that are not using MIDI.
OOOoo, I just found a good one... Here is a tool that implements the Web MIDI API using the Jazz plugin. With this I can use the Web MIDI API as captured in the specification - the polyfill will automatically check to see if the Web MIDI API is already implemented, and if not it will insert itself.
The question is this: If you have a mobile device, can you help me get MIDI working on your device? Ideally we could exchange email addresses, and I could send you links (at readmusicfree.com, or other sites that use the new Web MIDI API), and you would tell me if they work.