If memory serves, my very first wrestling match as a kid was watching an Ivan Putski and Tito Santana tag team match.
Garea and Martel
The Wild Somoans
Fuji and Siato
Windham and Rotunda
The Von Erichs
The Freebirds
The Midnight Express
Tully and Arn
The Rock and Roll Express
Dusty and Magnum
The Road Warriors
The Midnight Rockers
Ivan and Nakita
The Steiner's
Dusty and Nakita
The British Bulldogs
The New Age Outlaws
The Hardy's
The Dudley's
Edge and Christian
and so many many others over the years
I openly weap having to watch New Day and The Ascension now. I think we have hit rock bottom :(
Tag team wrestling has been greatly de-emphasized, but I don't really blame the performers there as much as the booking.
The Ascension could be every bit as good as a team like Demolition was, but are treated like jokes, so they are viewed that way. New Day(preferably Big E and Kofi) could be great, but are given nothing to do, which baffles me, because Kofi is/was very popular(especially with kids) and Big E was a can't miss prospect, who somehow has missed.
Currently, I think the Usos are the biggest problem with the tag division. Mediocre matches, and no character, and the same move sets is a recipe for boredom. Kidd-Cesaro could be amazing as tag champs if they commit to them. But really tag team wrestling has been stagnant ever since The Shield broke up, and predictably hasn't been a focus since.