During my time as a wrestling fan it has to be The Hardy Boyz v The Dudley Boyz v Edge & Christian, or any comibnation of those 3 teams. The number of great matches they gave us was phenomenal, and their feud was a definite high point for tag-team wrestling in WWE, which is likely never to be seen again.
The Hardyx and E&C had already been involved in a great feud, including the first ever tag-team ladder match (which is still arguably the greatest match I have ever seen), but when the Dudley Boyz joined WWE, the rivalry was taken to another level, culminating in the series of triangle ladder amtches, TLC matches etc that are still mind-blowing to this day.
5 of the 6 men ended up as World Champions, including Edge who is the most decorated wrestler in WWE history, and every single one of them was crucial to this rivaly as they all worked incredibly well together, took insane career-shortening risks and bumps and gave us memories to last a lifetime.