My almost 50-year-old daughter still plays her Hudson Brothers records, and Friended one of them on FB awhile back. 
Their show was a lot of fun.
I remember watching these “name” variety shows but won’t swear it was in the 70’s:
Smothers Brothers
Sonny & Cher
Johnny Cash
Dean Martin
Jimmy Dean
Ah, and the guy with the attack emu puppet! Loved it!
Rendezvous, ren-ren-ren-rendezvous…
Remember The Jacksons variety show?
The Barbara Mandrell show with all of her sisters. Corny but we loved it.
Everybody loves mime, right?
The Bobby Darin Amusement Company - 1972-1973.
♪ ♪♪ Oh, the shark, babe,
Has such teeth, dear… ♪♪ ♪
The Harlem Globetrotters Popcorn Machine
The Jimmy Dean Show (which gave Jim Henson his start)
The Richard Pryor Show
Your Show of Shows with Sid Caesar and Imogene Coca; writers Mel Brooks and Carl Reiner
Do they count as two since they had the Saturday morning show, and an evening hour at one point?
Tom Jones was on ABC Friday nights from 8:00 to 9:00, CT, just before The Avengers came on. This had to be well before 1969, since I used to hurry home on my bike each week to watch them in the summertime.
My favorite variety show in the late '60s and early '70s was Dean Martin’s. Loved him, loved his guests, loved the Golddiggers. The clips from his show on YouTube still send me into hysterics!
Jimmy Dean? My God, he was on when I was in third grade, well before the '70s.
Cher
Shields and Yarnell
That was your aforementioned Tony Orlando and Dawn.
The Glen Campbell Goodtime Hour!
Ah, the emu… totally forgot about that.
Not to mention the Sonny Comedy Review.
Speaking of Saturday morning variety shows, there was also the Bay City Rollers Show.
I remember my babysitter insisted on watching an episode of it (while she was sitting us one Saturday night) because Howard was hyping an appearance by “Chicago”, which was her favorite band. Finally, late in the show, it turned out it was actually a number by the cast of the Broadway musical. Man, was my babysitter pissed. 
From what I remember, it was a lot like (and probably was meant to be a lot like) the Ed Sullivan Show.
Was that where I first saw The Mighty Favahd (sp?) sketches? Those were hysterical.
The Mighty Favog was on the first season of SNL—which early in its run had more of the feel of a classic variety show than what it later evolved into.
The Original Amateur Hour (1948 - 1970) just cause it did it early.
Hee Haw (1969 -1970) Buck Owens and Roy Clark.
Sha Na Na.