Cheap Trick, Eagles, Tim McGraw, Prince, Third World, America, Hank Williams Jr, Harry Conick Jr… all about the same number of times.
If Vegas/Branson type acts count, Jim Stafford, Shoji Tabuchi, The Baldknobbers. Numerous times.
Hands down winner, tho, is the Houston Symphony Orchestra, dozens of times. Since performers change in an orchestra, tho, probably not quite what the OP wanted.
Five way tie:
KISS
Natalie Merchant
Paul McCartney
Heart
Journey
I’ve seen all of them once.
I don’t have an “official” count for Allman Brothers concerts anymore, but I think I’ve seen them 67 times.
I’ve seen Bob Mould at least 22 times, I lost count but it’s probably a few more than that. I’ve only missed one show I could have attended (that I knew about).
Whoa, how can you afford your rock & roll lifestyle? 
Jethro Tull, about 25 times I think, plus a couple of Ian Anderson solo shows.
I was hoping to catch Mould at Riot Fest in Chicago a few weeks ago but we weren’t able to get back into the city in time for his set. Seeing The Replacements (and The Pixies) made up for it though.
Freaking awesome! I was AT that Moline show! I had 7th row seats on Alex’s side. Primus opened up and Alex came out in a sheet to play trumpet (screw around trumpet)! I missed getting a stick by about 2 feet.
If I’m counting correctly, I’ve seen Rush 7 times. Every tour from A Farewell To Kings to Grace Under Pressure, then about 25 years later on the Time Machine tour.
Richard Thompson and Old 97s come in second at 5 each.
Bands I’ve seen more than 10 times:
Tori Amos
They Might Be Giants
Bands I’ve seen between 5-10 times (possibly more):
Ani Difranco
Ben Folds/Five
Moxy Fruvous (most people haven’t heard of them, but I’m including them anyhow.)
Great Big Sea
Cracker
It’s sad that I think I’m forgetting some…
It is difficult.
I’m pretty sure the only group I’ve seen in concert more than once has been The Pat Metheny Group. Twice. Both times in Nashville.
I might count The Wooten Brothers but one of their gigs was a wedding reception.
I’ve seen about 50 bands/performers as many as four times, including The Beatles in '65, my first ever concert.
Anyway, my most seen act is: The Doors. Five times. 1967, '68, '68, '70, and (post-Jim) in '72.
Saw the Grateful Dead 10 times, but I’ve seen Widespread Panic about 25 times.
I saw The Smiths 8 times, largely due to youthful exuberance in following them round on a Scottish mini-tour they did for the Meat is Murder album.
I’ve probably seen Teenage Fanclub about the same number of times. There was a period where they seemed to support just about every decent US band that played in Glasgow. The only time I think I’ve seen them where they were top of the bill was when they did a show with Alex Chilton.
It’s been so long since I’ve seen either group that I can’t come up with an official count right now. But I think I’ve seen Ben Folds/Five and the Squirrel Nut Zippers maybe 8 times each? At least that, or more.
I saw the Moody Blues a lot too when I was younger, maybe even 8 times for them.
Other than local bands, I think Pearl Jam is the only other band I’ve seen more than once (3x).
Wow, I used to be a ticket scalper and have come nowhere close to seeing anyone 20+ times! Some of you folk are seriously dedicated fans! 
For me it’s Aerosmith (7 or 8 times) and what’s weird about that, I’m not really that big of a fan. It’s just a fluke. It seems like every time Aerosmith comes to town, somebody in my circle has an extra ticket and wants me to tag along.
Grateful Dead at least 50 times. Still have the tickets stubs for most of them. Know people who have seen them in the hundreds of shows.
One of my biggest musical regrets was not seeing MF before they ended their run. They were in Seattle right around the same time TMBG had a show scheduled (Mink Car tour, I believe) and I chose to see TMBG since I had been a fan of them much longer and hadn’t seen them yet. Never got another chance to see Fruvous.
Does it really count when she plays at your house though?
I’ve seen Motorhead the most, at least 10 times, once two nights in a row.
I’ve seen Iron Maiden 5-6 times.
Rush 3 or 4 times.
Judas Priest 3 times I think.
And a bunch of bands 2-3 times. I’ve stopped going to concerts a whole lot, the last time I saw one was like 4 years ago, and it was Motorhead.