Across the Universe had some good covers. My favorite was the movie version of I Want You (She's So Heavy). The sound track version unfortunately has Dana Fuchs singing and her voice is akin to nails on a chalkboard.
I've never been a huge Beatles guy, for whatever reason. I like a lot of their solo stuff (especially George Harrison) but not much else. However, I do like Beatles covers a lot, and I think this will always be my favorite:
Siouxsie's one of my favorite artists ever and I think she really does a great job of turning this into an amazing goth/pop song.