Amusingly, when I posted the poll, I had one answer in mind. I kept remembering things, though, and adding to the list, and when I was done there was a different correct answer. I started with 22 in my mind as the correct answer, but I'm currently at 26. I've probably forgotten something.
Binion's - about a zillion times, and I'm sad that it's closed.
Four Queens - a couple of times, including one hellish experience with two "broken" rooms, a migraine, and being right above the Fremont Street Experience
Golden Nugget - recent BARGEs/EMBARGO
Plaza - a couple of times, one while Greg Raymer won the WSOP
Main Street Station - quite frequently
Orleans - quite a lot, Orleans Opens, BARGE, TOC, and lots of just-for-fun trips
Rio - several times, but not recently
Gold Coast - occasionally when other things were booked
Boulder Station (or something out that way) - my first Vegas trip a couple of decades ago
Hilton - a couple of times, but I barely remember why
Flamingo - I know I've stayed here, but I don't remember when
MGM - with an ex, many years ago
Mirage - during TARGET once. I hate the Mirage with a passion.
Treasure Island - with a friend once. I'm not a fan.
Palazzo - after BARGE, the Venetian sent me lots of free rooms, and I stayed at both properties
Venetian - see Palazzo
Casino Royale - during BARGE at the Venetian
Paris - with my old housemates, though I don't remember how it happened
Riviera - for backgammon tournaments. I was here during an earthquake once.
Some dive next to the Riviera - got stuck here one night. It was horrid.
Stardust - I had one of the most valuable conversations of my entire life while waiting for a cab here
Sahara - once or twice during TARGET
Tuscay - while attempting to take advantage of a casino promotion
Non casino hotels:
Budget Suites out Boulder - stayed here for the whole 2003 WSOP
Budget Suites by the Orleans - once, I don't remember for what
Some business-traveler-type hotel south of the airport - a friend was in town for Comdex, and suggested I come hang out with him. It was unremarkable.