A place to host static HTML+JavaScript that can be referenced from a paper? My PhD supervisor always told me that we write papers "for the ages". The publication system being what it is, we cannot go back and update any links, so we should not cite or reference a source that may be gone in five years.

With that in mind, I'm looking for a place to host a small open-source web-application, consisting only of static assets (HTML, CSS, JavaScript), and I would like to link to it from my paper. GitHub being as big as it is, I suppose I will trust them for storage, but they do not offer hosting. Ideally, someone reading the paper should be able to go right to a URL and run the app.

Any thoughts?
GitHub Pages web hosting really is perfect for your needs, but you might also want to consider FigShare. You'll get a DOI, which makes it easy for people to cite your HTML application. You could zip up your application using only local references so your app will be downloadable and usable as long as HTML 4/5 browsers exist. Until March 2015, content on FigShare was shared through an international alliance of libraries (CLOCKSS), but alas no longer.