Ubuntu, like any modern Linux distro I suppose, has done reasonably well on the accessibility front. Various accessibility tools are available, as they would be on Windows or OS X. But the biggie that people have been wanting on the Linux desktop was not so much for a screen reader, which is already quite good, rather access to a usable voice activated desktop interaction system.
According to this thread from the Ubuntu forums, the application known as VEDICS is going to be making its way onto the desktop. I have used it and I will admit, it’s very good. While it’s not perfect all the time, I have found that VEDICS will do well for most people using a good noise canceling mic with a clear knack for spoken English and you’ll do fine.
Now for the really cool part. In addition to being able to manage much of you desktop with nothing but your mic, soon you’ll be able to do dictation much like you might see with Dragon Naturally Speaking on the Windows platform. While it may still be a work in progress, it’s coming along very nicely and based on the demos seen here, you’d be hard pressed to beat it.