1) The Four Horsemen/Evolution--Some may call this a cop out, but Evolution followed the formula that made the Horsemen successful. I basically look at Evolution as the WWE's resurrection of the greatest stable in wrestling history. Every time the Horsemen showed up, they dominated (less the Flair, Benoit, Mongo, Malenko group formed as an attempt to save WCW in its dying days).
2) The Heenan Family--I was only able to see the final years of the Heenan Family due to my age, but I have seen a great deal of videos (many thanks to YouTube) and can respect what Bobby Heenan did. IMHO, he's the greatest manager in wrestling history. In many ways, this was the first stable. The family lasted over 2 decades and had many greats: Nick Bockwinkel and the Blackjacks in AWA; Andre the Giant, Mr. Perfect, Rick Rude, Big John Studd, Paul Orndorff, Harley Race, and the Brain Busters in the WWF.
3) nWo (Hogan, Hall, and Nash)--The original idea behind the nWo was brilliant. These guys were legitimately seen as invaders attempting to overtake WCW. The feud with Sting and constant question of whether or not he would join was compelling television. The problem is that it grew in size and became stale quickly. Had it just stayed as a small group that dominated the title scene, the nWo could have had a more lasting impact...PS, the WWE version was a failure in large part because of WWE fans' inability to accept Hogan as a heel.
4) D-Generation X--The first faction to make the list that is remembered primarily as faces. In its first two incarnations, DX was involved in feuds with the three great heel stables of the early Attitude Era (Hart Foundation, Nation of Domination, Corporation). Along with Steve Austin, DX was the face of the WWE for several years.
5) The Corporation/Corporate-Ministry/McMahon-Helmsley Regime--The Attitude Era was defined by anti-heroes fighting against the evil corporation that ran WWE. Headed by various McMahons over the years, rivalries and partnerships with the Corporation were responsible for creating the three biggest stars of the Attitude Era (Stone Cold, Rock, and Triple H).
6) Hart Foundation--Responsible for cementing Bret Hart as a heel character in the States, while remaining an over face stable in Canada and Europe. Rivalries with Steve Austin and DX helped push them to main event status and usher in the Attitude Era.
7) Nation of Domination--The Rock's heel turn was what made him great, and the Nation was the breeding ground for his new persona. The memorable with DX in 1998 was some of the best programming done in the Attitude Era.
8) The Ministry of Darkness--The key to The Undertaker's heel turn in the late 90's early 00's. The bizarre rituals such as crucifying various wrestlers (and Stephanie McMahon). The Undertaker answering to a "higher power". The stable was essentially a satanic cult. It seemed that there was no way for Vince McMahon to stop them, until it was revealed that he was the "higher power" that the Undertaker answered to.
9) Legacy--Cemented Randy Orton as one of the greats of the era and began establishing Ted DiBiase, Jr. and to a lesser extent, Cody Rhodes as future stars of the company.
10) Million Dollar Corporation--Ted DiBiase's final attempt to use his money to control the WWF (for now, I'm hoping something happens with him and his son(s) in the near future). What really made this group stick out to me was the number of kid friendly faces that turned and joined Dibiase.