This answer is from 2013. Other (maintained) solutions exist now - some of which are mentioned in answers below.
Original answer:
Maybe a bit late but after I came across this problem I found there were still no tools to do this. So I forked the TS compiler and created the code to do it.
Forked TypeScript compiler project at v0.9.0.1 then added a "--documentation" option that will generate wiki documentation from whatever JSDoc you put in the code (none required for just plain output of methods/properties etc. )
It produces .ts.wiki files (contents of which is suitable for uploading straight to CodePlex etc. if you also use the new --wikiRemoveRoot and --wikiSourceRoot params as well - see fork - my first commit description). Or you could adapt the code to produce HTML (which would be relatively simple - I've done the hard work of mangling the compiler/delcrationEmitter :) )
Hope this helps (either you or future readers of this question)
Ed