Too many shows (500+) to name just one, so:
Most "Memorable": Eric Clapton, August of 1974 on the "461 Ocean Blvd" tour. Peter Townsend and Keith Moon showed up and joined in on the fun.
Most "Impressive": A tie between a) Jeff Beck, October of 1980 on the "There and Back" tour (Michael Stanley Band opened) or Talking Heads, August of 1983 on the "Stop Making Sense" tour. That concert film only hints at how incredible that show was.
Most "Unique": Jim Carroll, November of 1983 did both a poetry reading and concert at the Detroit Institute of Art.
Most "Intense": Hunters & Collectors, May of 1987 on the "Human Frailty" tour. They literally blew the roof off of that venue.
Best "Headliner/Opening Act" combo: Bonnie Raitt & Rchard Thompson, June of 1989. "Nick of Time" & "Amnesia" tours. "Nick of Time" had not quite broken through yet and RT probably made a lot of converts that night. Stylistically, this was an ideal combination.
Most "Emotional": The Blue Nile & Wendy MaHarry, August of 19990 on the "Hats" tour (Wendy had only released her debut LP). This show was literally a "spiritual experience." I'm pretty sure that was the only national tour of the USA for both artists.
Most "Sensual": Sade, September of 1993 on the "Love Deluxe" tour. The air was so thick with pheromones that you could cut them with a butter knife.
Most "Medicated": Pink Floyd, July of 1973 ("Dark Side of the Moon" tour) and May of 1994 ("Pulse" tour).