Primus has done it several times. They've performed Sailing the Seas of Cheese, Frizzle Fry, Pork Soda, Green Naugahyde, Wonka, and Desatruating Seven. Most recently, they toured performing Rush's "A Farewell to Kings" in its entirety. Les Claypool's Frog Brigade is gearing up to perform Pink Floyd's "Animals" this Spring, which they also did 20 years ago.

I've seen Steely Dan perform Aja in its entirety. They were doing a tour where they would play it one night, then The Royal Scam the next.

I once saw Roger Waters perform Dark Side of the Moon. He's also toured The Wall.

I also once saw Reel Big Fish perform Turn the Radio Off except they skipped Beer and saved it for the encore.

They Might Be Giants tour performing all of Flood (sometimes in reverse order) every few years.

Many years ago, Weezer toured performing Blue Album one night, then Pinkerton the next.