To make my pick in this, I am ignoring the likes of Animal/Hawk, or the R&R Express. This is because while they were definitely phenomenal teams, this isn't about TEAMS. it's about individuals, who work well in a team. Its all well and good being phenomenal with one partner, but I am looking at someone who has had alot of success with numerous partners- showing their versatility and abilty to adapt and still win matches.
The first 2 names that jumped out at me were Edge and Kane, due to the number of reigns they gathered in their WWE careers, and the number of partners they worked with.
Edge is the most decorated WWE wrestler of all time when looking at titles won, and while I don't think he should have had as many runs with the World Titles as he did, there is no doubt he was an amazing Tag-Team wrestler. As part of the legendary Edge & Christian team, he won the Tag Team titles on 7 occasions and was one of the innovators of the Ladder and TLC matches for Tag Teams at a time when the WWE had a very strong Tag Team Division. He won the titles again with Hulk Hogan who was a totally different kind of partner to Christian, twice with Chris Benoit and once with both Chris Jericho and Randy Orton.
This gives Edge a total of 12 Tag Team Title reigns with 5 different partners
Everyone thinks of the "Brothers of Destruction" Tag Team when thinking of Kane, but they forget just how many tag-teams he has been a part of. Kane did indeed hold Tag Team gold 3 times with The Undertaker (2 WWF and 1 WCW) but he also won the Tag Team titles with Mankind on 2 seperate occasions, twice also with X-Pac (that was a really entertaining team in which Pac was bringing out the more human sign of Kane), once with Rob Van Dam, once with The Hurricane, once as part of Team Hell No with Daniel Bryan and twice with The Big Show.
I already knew Kane had worked with alot of partners, but the number actually surprised me. In total Kane has 12 Tag Team Championship reigns under his belt, with a total of 7 different partners.
In my opinion this makes KANE the greatest Tag Team partner of all time. He's had vast success over a 15+ year period, working with his own flesh and blood in The Undertaker, big man/small man teams with X-Pac and Hurricane, powerhouse/High flyer team with Rob Van Dam, 2 very dysfunctional teams with Daniel Bryan and Mankind and in teams comprised of 2 giants with Big Show and 'Taker. The variety of partners and styles of team he has been a part of, which have all brought him success makes Kane my pick.