Rhapsody in Blue - Which one?

Buy them all. I do not really have a favorite and I really have never thought that way as it is tooo black and white. However I have one that I believe is a Telarc that also features "Catfish Row" that is excellent. Really, you should look at each as a different interpretation, each with it's own perspective and each representing a certain truth. That way all of them together represent the total of humanities attempt to understand Gershwin and then each will give you a greater perspective on Gershwin and hopefully a greater respect and understanding of his unique place in the small pantheon of great American composers. What I like to do is play him and then play some Copland as they are contemporaries while one represents a love for the city and the other a greater appreciation for the more not city. You know yen and yang kinda stuff. I'm not explaining this very well but you'll get it if you listen.

I agree with Kchahoc that this work can be enjoyed in many different interpretatations, and it would be a shame not to hear several. But, of the many different performances I've acquired over the years the two that get replayed most frequently, due to their superb energy, pacing and sheer fun, are:

Previn/London Symphony Orcehstra on EMI -- a delightful and characterful performance with excellent piano work by Previn and clarinet by Peyer.

Andrew Litton/Royal Philarmonia Orchestra on MCA

These recordings aptly demonstrate that it doesn't take an American orchestra to make this music work.

This was one of my favorite works until United Airlines ruined it for me. You can't avoid it whenever you go to any airport.
Having said this, I agree with above comments, there are many scoring versions of this that owning one does not do it full justice. There are full orchestral versions and the Whiteman's versions. One of my favorite is with Abbey Simon and Leonard Slatkin on VOX. They use a modified Whiteman's version, I believe. You can feel the atmosphere of the era. It simply transports me everytime.

Yeah, I like the old Bernstein as well. If memory serves, I believe he is the pianist as well as the conductor..

If you are really a quadophile, try the Litton on Delos.