Barry did a really beautiful, lush, orchestral version on a 1995 album called Moviola II: Action And Adventure (a small portion can be heard at the link). It may be my favorite version of it.
The film version was sung by Nancy Sinatra:
An alternate theme song (also called "You Only Live Twice" and sung by Lorraine Chandler) was discovered in the vaults of RCA records in the '90s. It was perhaps intended as a demo for consideration by the film's producers. It's sort of what a Bond theme would have sounded like if done by Martha and the Vandellas:
A completely different "You Only Live Twice," sung by an uncredited Julie Rogers, was featured on The Best of James Bond 30th Anniversary in 1992. Here it is:
And then there's also this intriguing theory about a Beach Boys crossover.
A recent cover was done by Natacha Atlas in 1999. It is on her 2005 compilation album The Best of Natacha Atlas. I think I like her's a lot more than Nancy Sinatra's. She really nails it!
Get used to this picture. Might there be a subliminal message? Can you imagine what that image did to men in repressed, strict Middle Eastern societies?? Is it just me? The point is, it's the only picture in this video, featuring her amazing interpretation of "You Only Live Twice" (it's so damn good):
Björk also recorded a cover version for an album of Bond theme song covers done by current acts. Hers sounds a lot like Natacha Atlas'. In fact, it sounds kind of like Natacha Atlas' voice was erased and Björk's put in its place. Whatever, she does have quite a set of pipes, despite possibly being a complete koo-koo bird. According to this site, she withdrew her contribution from the project.
Coldplay did a rock version while on their 2001 tour.