Rush, Grace Under Pressure Tour
October 2, 1984 The Centrum, Worcester, Massachusetts
Grateful Dead, about 15 times. If I count the shows that the various members did in different incarnations after Jerry died, it probably goes up to around 25-30.
Oh and band Ive seen the most is Phish at 21 shows, which doesn’t come close to most of their fans.
Embarrassingly enough the first concert I went to was Leo Sayer…mid 1970’s I’d guess. There’s no accounting for taste but I managed to redeem myself for my second concert…Rush, Max Webster, Triumph (I think) and Ian Thomas…for $15.00!
Van Halen 1984 Tour (a few weeks shy of my 16th birthday)
April, 1984 Brendan Byrne Arena (now the Izod Center) in the Meadowlands Sports Complex, East Rutherford, New Jersey.
ETA: I saw the Dead Kennedys before that, circa 1983, but it was in a club in Manhattan and that probably doesn’t count as a “concert”.
Rush, December, 1981, “Exit…Stage Left” tour.
I don’t know what band I’ve seen most - probably a small celtic band, either The Elders, Enter the Haggis, or Seven Nations. In terms of big well-known bands, I’ve seen NIN three times, Queensryche four, Ozzy probably four, and random various 80s hair bands a bunch.
Glad I wasn’t the first to say it.
The Beatles. San Diego, August 1965. I was 14.
Ozzy Osbourne at the Capital Center (Landover, Maryland) in 1988. I was 13, and my mom was not happy.
The artist I’ve seen most often would either be Bob Dylan or Fugazi - 15 to 20 times each.
I’d count it.
Act or group I saw most often:
The Doors.
Late 1967, mid '68, late '68, mid '70;
and after Jim’s death in mid '72.
.
We are not worthy. We are not worthy. We are not worthy.
Alice Cooper, early 70’s in Florida. I’ve seen him twice.
I feel lucky to have seen Lynyrd Skynrd not long before the plane crash that killed Ronnie.
Again, please. 
Styx, three times.
First concert - Ratt, LA Guns and Band Tango.
Most often - Poison
I am not ashamed of these shows - I love me some hair metal.
However, I would like to regain some credibility - My second place, most often is Steely Dan. 
The second concert I attended was Motorhead, in Madison, WI, in December, 1985. They played in a gymnasium (I kid you not). We were no more than 25 feet from the amps. I suffered significant hearing loss that night. 
Is that Bang Tango? I thought I was the only one who’d ever heard of them.
Yes! It’s Bang Tango.
They were terrible, IIRC.
But LA Guns was terrific.
We are not worthy!
Seriously, I’d probably have donated a major organ to have seen either of these bands. I’m awestruck. And gobsmacked too.