There are so many individual performances from numerous Ring cycles that I would never want to be deprived of, but I agree with chefti that for overall balance of sound and interpretation the 1955 Keilberth Bayreuth set takes the cake. All the chief singers are great artists. Hans Hotter commands the role of Wotan as no one ever has, and rises to all the great climaxes with astonishing steadiness and power. Wolfgang Windgassen, all told probably the most sympathetic and tireless of post-war Siegfrieds, is unstinting in this killing role, and at crucial moments truly heroic. It seems Keilberth was generally thought of as a somewhat sub-par conductor when he was alive, but his reputation has deservedly risen, and now listening to his conducting it makes one wonder why he wasn't always more highly regarded. Here he shows a consummate sense of timing and a wonderful flair for the dramatic. And I think it's worth getting the alternative Walküre and Götterdämmerung with Martha Mödl as Brünnhilde to hear the contrast between her and Astrid Varnay's awesome portrayal. There are several cast overlaps with the famous Solti recording obviously, though in my opinion Keilberth's interpretation is far better on the whole, and the singers are also in better voice.
Now if we were to pick out favorite recordings of each individual segment to make a dream Ring, that would be interesting. Just impulsively, maybe Solti's Rheingold, Leinsdorf's Walküre with Nilsson and Vickers, Keilberth's 1955 Siegfried and Furtwängler's 1950 La Scala Götterdämmerung?
