I always liked the Fantastics a little better than the Rock and Roll Express. Ricky Morton did the face-in-peril better than anybody, but I think the Fantastics were more interesting as far as their offense.
I liked the Sheepherders before they became the Bushwhackers--they used to be an incredibly violent team.
My three most important teams are The Freebirds [the original ones, of course], The Road Warriors, and The Midnight Express. I love a lot of the other teams people have mentioned, but I think those three each bring something to the table that was unique and original for their respective times, and each were a major influence on those that came after them.
Y'all are gonna smack me for this but the Hardy Boyz are my favorite tag team ever. Nobody does "Holy shit" better than Jeff, Matt has decent ground skills, and they both have that nebulous "it" that's so important in sportz entertainment. I honestly think Jeff Hardy may be the next Mick Foley.
Honorable mention goes to Cactus Jack & Mikey Whipwreck (seriously!) Edge & Christian & The Dudleys (probably equally responsible for the Hardyz' success,) Shoji Nakamaki & Hiroshi Ono (Two of the best, and most underrated, hardcore Puroresu guys ever) and of course the TAG TEAM CHAMPIONS OF THE WOOOOOOOOOOOOOOOOOOOOOOORLD! The New Age Outlaws... even my ex-roommate, who hated wrestling, got a kick out of The Road Dogg.
Everything's cool when you're Yun [point] Cheol [point] Su [point]
God knows I can't resist the chance to do some gratuitous listing, baby!
My favorite tag-teams, in no particular order:
Benoit & Malenko - The three way feud with Raven/Saturn and Kidman/Misterio is probably one of my favorite tag feuds of all time. Benoit and Malenko were in a monster heel groove at the time, spitting on the faces, blowing snot on them, and beating the holy hell out of anything that moved. Combine the fact that it's two of the best technical wrestlers ever on the same team and you've got gold. I still can't believe the WWF didn't make them tag champs before Malenko retired.
Raven/Saturn - See above, somewhat. Plus, Raven and Saturn are both two of my all time favorites.
Misterio/Kidman - Uh, ditto.
Midnight Express - Classic old-school heels, plus I always enjoy a good dose o' Cornette. Hell, that's half the reason I watch HWA TV every week...
Demolition - I remember walking around my backyard as a kid, singing their themesong at the top of my lungs. God, I was a dork.
Hardy Boyz - Sure, they've gotten a little tired, but Jeff can still make me wince with his bumps and Matt ties it all together quite nicely. Lita makes from some good eye-candy on the side, too.
Edge & Christian - Probably the funniest team ever, and both seemed to have a better workrate as a tag team than either do as singles. If they went back to teaming and never split up again, I wouldn't care.
Rockers - The prototype pretty boys with the nastiest break-up. One of the few old school teams who I think could still be successful in today's environment.
I never got to see the Hollywood Blondes, sadly, but I've heard great things...
And, for brief, marriage-of-convenience teams, I must admit to digging Kane & Mankind. I don't really know why, but the two of them together was just scary, man...
"All I ever asked for in life is an unfair advantage." Microchip, Punisher Annual #2