Road Warriors: Probably the most popular and best remembered team of the 80s, had their greatest run in the NWA as constant enemies of the Midnight Express and Four Horsemen, but also had much success in the AWA, WWE, and Japan.
Tully Blanchard/Arn Anderson: One of the best examples of two established singles stars forming an excellent team AFTER their singles success. These two were a great combination of off the top rope, technical, and brawling skills with plenty of creative cheating as heels. First tag team ever to win both the NWA/WCW & WWE Tag Titles.
Rock & Roll Express: Hugely popular in the 80s but also extremely talented, they wrestled against heavyweights while wrestling like cruiserweights with a wide array of high flying moves. The crowd reactions they drew were un real, and their feud with The Midnight Express was so good WWE copied the whole dynamic when the created the evil cowardly (but supremely skilled) Hart Foundation (complete with their own obnoxious southern manager, ala the Midnights) vs British Bulldogs.
Midnight Express: One of the greatest heel teams of all time, had a small rotation of members, Bobby Eaton, Dennis Condrey, & Stan Lane (who also excelled as fan fave in The Fantastics) being the primary three. So detestable were they that literally the only way to turn them face was to create another Midnight Express (lead by Paul Heyman) to destroy them.
British Bulldogs: Top face team in WWE in the 80s
Hart Foundation: Top heel team in 80s WWE eclipsing teams lead by Mr Fuji & Freddie Blassie
Harlem Heat: They dominated, exclusively in WCW, during a time when tag teams in general weren't doing much, still they dominated for several years, and their title success was hard to deny.
Personally Im not partial to Demolition, they were too much a rip off the RW, while the Bulldogs-Harts dynamic was based on the Midnights & R&R, it wasn't a carbon copy. And while they had a nice run it wasn't as prolific or as long as the other teams listed.
Rockers (AKA Midnight Rockers) - Had their best success in the AWA as that promotions copy of the R&R Express, copied the look and ring style, only not as well. In WWE they were mostly mid carders and never won a title. HBK's singles success and success in DX far outshines them.
The Outsiders in my view didn't spend enough time as an actual tag team, they were two prominent members of the NWO who teamed from time to time, they didn't compete full time and exclusively as a team they way Anderson & Blanchard did during their run, or the way HBK & HHH did in the 2000s when they reformed their shortened version of DX and won the WWE Tag Titles. To me they are comparable to Ric Flair's teams with Lex Luger (The self proclaimed "Dream Team) in 1987 or his run with Arn Anderson in 1990 & 1996, short term runs built into their bigger singles careers.
The Steiners were extremely popular, won a boat load of titles, and competed successfully in WCW, WWE, & Japan, and at their peak were extremely talented. I can see them being HOF worthy.
The Dudley Boys were by far the biggest tag team in their time, maybe not a great era for tag teams, but their whole ECW styled "get the tables" gimmick was revolutionary for its time.