WWE Tag Teams died when they RELEASED THE DUDLEYZ.
That is pretty much the case. Ever since then tag team wrestling hasn't been the same in WWE. Only teams that stick out post 2004 are London and Kendrick, Cade and Murdoch, MNM, and the Miz and Morrison. Most other tag teams were random match ups of two superstars or a team who just won the belts once then were never heard from again (Spirit Squad, Deuce and Domino, Colons, Hawkins and Ryder)
That is pretty pathetic, and even the above teams weren't around for long which is sad for a tag team. A successful tag team has to be around for more than I would say 3 years or so.
Miz and Morrison were also a team that was thrown together. Sure, they meshed well, but they were thrown together all the same.
From 2005 to early 2007, the tag team division was booming. No odd couples real fucking teams. Anyone remember:
The Dicks
The Heartthrobs
Gymini
Cryme Tyme
KC James and Idol Stevens
La Resistance
Pitbulls (Kash and Noble)
Highlanders
MNM
Bashams
Mexicools
Deuce and Domino
FBI (Little Guido and Tony Mamaluke) WWECW
For the majority that list is full of jobbers.