For me, the list would start out as:
1. Hogan
2. Ric Flair
3. Austin
4. Andre the Giant
5. Lou Thesz
6. John Cena
7. Undertaker
8. Bruno Sammartino
9. Triple H
10. Shawn Michaels
11. Sting
12. Bret Hart
Hogan should take the top spot for bringing the WWE into a new era in the 80's. He was very popular prior to that in the AWA, and his heel persona along with the NWO brought WCW, then seen as the distant number two wrestling promotion, to the number one spot for quite a while.
Flair is number two because whereas Hogan was the WWF in the 80's, Flair was TNA/WCW. Flair brought the wrestling part of pro wrestling with excellent matches, while at the same time brought the entertainment part with excellent promos. He was the WCW.
Austin gets three because he helped bring the WWF/E from the verge of bankruptcy to the main stream. Vince obviously had a huge hand in that as well, but it is Austin who will be remembered for decent matches, excellent promos, and being the guy who revolutionized pro wrestling in the late 90's.
Andre the Giant was THE wrestler in the 70's. His size and presence brought immediate credibility. His drawing power was obvious when he faced Hogan at Wrestlemania III. It is a shame that most people will never know much about Andre and that decent footage of his matches will never really surface save for the late portions of his career when his career and his body were both winding down. However, one need read virtually any wrestling autobiography to know of the legacy this man had.
Lou Thesz was pro wrestling when he was around. He loved it and was an excellent wrestler who would never have lost...aside perhaps when facing Andre. Lou reportedly looked the part, suit and tie, and represented pro wrestling as a professional sport rather than entertainment as it is now being represented.
John Cena has been the WWE's torch bearer since he got the strap in 2005. In mid to late 2004 he was already becoming popular and now is the WWE's image. The fact he held the world title for over a year during an era of month to three month title reigns speaks volumes. Furthermore, like it or now, he is the face of pro wrestling for the past decade.
Undertaker has been around for two decades in the WWE and has managed to reinvent himself successful during each of the auras. He has faced all the top stars and held numerous titles. Undertaker may not have been on the level as Austin or Hogan in that he brought pro wrestling to a whole new level, but he has been a consistent force to be reckoned with throughout the years and where many other stars faded away because they couldn't change with the times, managed to give new dimensions to his character while not betraying its roots.
Bruno was the face of pro wrestling for the WWE in the 60's and 70's, with perhaps the exclusion of Andre. His star power immediately brought fans to the arenas. He was a wrestler that fans, especially in the north-eastern states, could identify with. he was Vince McMahon Sr's go-to man, with again perhaps the exclusion of Andre.
Triple H is a variation of this generation's Ric Flair. However, that does not mean he is this generation's Ric Flair. Unfortunately, this generation's Ric Flair probably is in the form of several wrestlers. Nevertheless, Triple H was dominant the past decade, picking up numerous world titles and facing many of the top WWE, and eventually former WCW stars in matches. He was part of several huge stables including DX, Evolution, and the Helmsly-Mcmahon alliance. In addition, he is married into the McMahon family meaning he will have an influence in pro wrestling for years to come. The reason though he is where he is at is through he was dominant, he didn't bring wrestling to a new level like Hogan or Austin did, be the mainstay of the company like Ric Flair, or be in it as long as the Undertaker and successful. This may change though as ten or twenty years down the line, who knows what decisions Triple H may make that will forever change the landscape. Give another decade and given this man's accomplishments in the ring and outside of it (but influencing it), he could take the number one spot.
Shawn does not deserve the number one spot. Shawn had a wonderful career, had many excellent, match-of-the-year matches, and was one of the founding fathers of the "attitude" era. He was the next man in line after Bret to carry the WWE's torch. Unfortunately, his "12 year old boy's dream" clashed quickly against fans who were much more interested in men like Austin. It made his first world title reign, while decent in terms of wrestling, fairly insignificant in term of changing the landscape or leading into the future. Shawn shouldn't feel bad though; this continued for a couple of more years until Austin won the title. Beyond that, though Shawn helped start the attitude era, he wasn't part of the biggest parts of it. Nor was he part of the WCW / WWE feud. By the time he came back, pro wrestling was on a down trend. Shawn did what he could, he had excellent matches, putting over talent when he needed to. Heck, even injured, he could have a great match (see him vs Triple H at the first Cyber Tuesday). Shawn was a mainstay, no doubt about it, but not quite on the level as the Undertaker.