Finnegans Wake is one of those books that just cries out to be read aloud. On the page it's complex, abstruse and downright impenetrable at times, but on the ear it's funny, mellifluous and full of punning surprises. If you haven't the heart to plunge into the deep end, take a look at the 'reduced' version edited by Anthony Burgess.
On reading aloud generally, I think that sometimes the authors themselves haven't the right voice. I've got a recording of Joyce reading from the Wake, and it's not a patch on some other, more 'actorly' renditions. And Richard Burton's voice, for me, is the voice for Dylan Thomas.