Nine versions of the Nibelungen Ring are commercially available on DVD, of which eight (save the Weimar Ring) are as of now extensively reviewed on this site.
In chronological order (ranking by my personal preference in the parenthesis):
1. Bayreuth 1980: Chéreau/Boulez
The legendary "Centenary Ring" from 1976, commemorating the centennial of the world premiere of the Ring. Notable for Patrice Chéreau´s very vivid and detailed stage direction. Even after 30 years this Ring shows no sign of aging. (Ranked: 2)
A better Walküre Act 1 I have never seen (Peter Hoffmann and Jeannine Altmeyer):
2. Metropolitan Opera 1989-90: Schenk/LevineThe only "traditional" staging of the Ring available on DVD. Though most agree it is a rather dull affair, for those placing major emphasis on "stagings Richard Wagner would recognize", this is the set to get. (Ranked: 6)
Below, Matti Salminen in Hagen´s Watch. If the entire Tetralogy was like this, the ranking would be significantly higher than 6:
3. Bayreuth 1991: Kupfer/Barenboim
Daniel Barenboim´s first assumption of the Ring in Bayreuth. Notable for the superb orchestra playing and for Harry Kupfer´s detailed direction and very bleak view of the work. Also known as the "Laser Ring", main features are an endless road and laser projections. (Ranked: 1)
Below, the greatest execution of the greatest scene in all of opera, no less. (John Tomlinson and Birgitta Svendén, Siegfried Act III prelude and scene 1):
4. Amsterdam 1999: Audi/Haenchen
The Amsterdam Ring is notable for the almost ethereal beauty of the sets, where Audi has extended the stage to all sides of the orchestra, placing the players in the middle. Much, however, is musically disappointing. (Ranked: 5)
Audi´s epic spaces come fully to their right in Götterdämmerung:
5. Stuttgart 2002-3: Various/ZagrosekThe epitome of the Regietheater Ring, dividing the Tetralogy between four directors and different sets of singers for the first time in history. Essential viewing for those with an interest in ground-breaking music theater. (Ranked: 7)
The beginning of Peter Konwitschny´s Götterdämmerung (Luana DeVol is a rather fine Brünnhilde):
6. Barcelona 2003-4: Kupfer/de Billy
Harry Kupfer´s second Ring assumption after Bayreuth. First shown in Berlin in the 1990´s. Notable for Kupfer´s approach, which centers around the World Ash. Musically, however, it is more than disappointing.
(Ranked: 8, due to the musical quality. Judged by the staging alone it would be number 1).
Kupfer´s gleamingly beautiful Rheingold:
7. Copenhagen 2006: Bech Holten/Schønwandt
Known as the "Feminine Ring", feminine aspects are not really dominating this Copenhagen Ring production, apart from in interviews. On stage, we see a Ring taking us through the history of the last Century. The musical quality is furthermore high. (Ranked: 3-4)
Promotional video with clips from all four operas (don´t miss the controversial ending):
8. Valencia 2007-9: Fura del Baus/Mehta