I knew I would never be near the top but I was hoping I could post earlier so my 11 times seeing Dashboard Confessional could be in the running for a bit. It would have been 14 or more if they weren’t in the habit of playing in the Orlando area during the holiday season, cause other plans interfere, sometimes even after I’ve already gotten tickets.
Heart and Saves the Day are tied at around 7 or 8 times apiece, although more than 20% of the SDMB probably have not heard of Saves The Day.
They’re a local Nashville group and do all sorts of gigs. Their fame hasn’t made them inaccessible, or at least it hadn’t back in the 90’s which is when I would have seen them at the reception. Their version of Over The Rainbow choked me up at the time and remains the version I think of first when that song is played.
Depeche Mode, 8 times.
Nine Inch Nails, 5 times.
For lesser known, VNV Nation (8 times).
Rush! No surprise there, eh?
I’ve only seen them live five times, so they barely beat Cheap Trick, THE Music Fest Greats of the 80s.
Either Bob Dylan or Neil Young (with or without Crazy Horse), both around 15 times.
I’ve seen Steve Miller Band and ZZ Top both 4 times. The first time I saw either of them they were playing the same show.
Two of my favourite bands that I’ve only seen live once and would LOVE to see again are Walk Off The Earth and the Sam Roberts Band.
Also, it’s great to see some Moxy Fruvous love in this thread. They were sort of before my time, and I’ve only recently discovered them on YouTube, and I envy anyone who’s seen them live. 
I’ve seen Pat Metheny either with his Group, Trio, or solo a total of 16 times.
Also:
Metallica 5x
Peter Gabriel 5x
Springsteen 4x
“Weird Al” Yankovic 4x
Ben Folds 3x
Sting/The Police 3x
…and all of the following twice:
Genesis
Squeeze
Billy Joel
Queensryche
The Who
I should give Guns ‘n’ Roses a special mention as the most famous band I’ve seen the most times without actually trying to. I’ve seen them twice as an opening act, once for Red Hot Chili Peppers (1986) and once for the Rolling Stones (1989).
Wow, I am hand-gnawingly jealous. I’ve seen Morrissey seven times as I was still a kid when the Smiths broke up.
I’ve seen Low probably 12-14 times. After that would probably be Trampled by Turtles 8-9 times. After that, I’m not sure… either Wilco/Jeff Tweedy or Bruce Springsteen at about 5 times each.
I didn’t expect to see Great Big Sea on this list. I’ve seen them four times. I wasn’t at all familiar with them until I married a Newfoundlander, and we’ve been lucky a few times in that our visits to my SO’s home coincided with GBS appearances on George Street in their home base, St. John’s.
The Black Watch pipe band. Twice.
Ooh, I’m jealous you’ve seen them in their native setting!
Winner for me: Grateful Dead (and various offshoots) - 24 times
Runner-up: Neil Young (with/without Crazy Horse and with/without Crosby, Stills, & Nash) - 8 times
Robyn Hitchcock (& the Egyptians/Venus 3/Soft Boys) - too many to count, but probably in the 30s
Bob Mould (& Sugar) - around 16 times
Saw Sleater-Kinney and Yo La Tengo every time they came around since the '90s (until recently for YLT)
A very odd tie with Greatful Dead and Metallica at five time each. BTO, Pink Floyd and Widespread Panic all tied at four each. Slayer, Motley Crue and Blues Traveler at three times per*. Too many seen twice to count. And many many more only once.
*Does Col. Bruce Hampton and the Aquarium Rescue Unit count?
Paul Weller, at least 8x.
I was going to say Sonic Youth - At least 6 times that I can recall.
But then I noticed Maserschmidt mentioned Reverend Horton Heat, and realized that yeah, people know who he is! I’ve seen him probably 20 times, an accurate number would be very difficult to gauge. I used to see him play at least 2 very long sets for $5 at the Library (a club named that, he didn’t play in a library) in Denton when I was in college. It was the greatest entertainment bargain to be had in my lifetime, I believe.
Marillion four times.(Three with Fish once with Hogarth)