The only exceptions are Google Maps or anything equally as rich. And I do mean equally as rich.
Like I said, Google Maps is my yardstick - anything less complicated than that should be built to work without Javascript. It might work slightly different and be a little less pretty, but there's no reason it can't work.
I read an interesting analogy in an article (which I have since lost and so cannot give credit) about accessibility: Oxo, the kitchen tools company, started by designing tools for people with arthritis. Having designed tools with nice soft rubber grips and large handles, they discovered that non-arthritic people really liked the tools as well, and now Oxo is sold at your local Target (and they are probably raking in cash).
Javascript is a great way to enhance the user experience, but you are being irresponsible if you develop sites that only work with JS enabled. It's seriously not that hard. Make it work first, then detect xhr on the server to add the nice partial updates, etc. And don't tell me it costs more money to do that. If it does, you designed it wrong or chose tools that are inherently inaccessible. In both cases the blame falls on you.
Full disclosure; I am a low-vision web application developer, born with congenital cataracts, along with my father and my daughter. Developers who use the excuse of "you have to have JS on for my stuff to work" make me incredibly angry, so I tried to keep this as civil as possible.