Metallica played Master of Puppets during a handful of select gigs on their European 2006 run.
Queensryche did Operation Mindcrime in its entirety, both on the Empire tour in 1991, and on several runs in the last, both as a special treat, and also to accompany Mindcrime II, also performed in its entirety.
Judas Priest recently did British Steel in its entirety.
Both Megadeth and Testament have been doing classic albums--Megadeth with Rust in Piece, and Testament with Legacy
Motley Crue did Dr. Feelgood in its entirety on the recent CrueFest 2 tour, and included a classic hospital stage setup.
Although not recent, the Who did Tommy on select dates for their 1989 tour, and did an entire tour focusing on Quadrophenia in 1996-1997.
Dream Theater has been no stranger to playing albums in their entirety, most notably Scenes from a Memory, and even Octavarium (as well as covers of MoP and NOT

. During several 2007 summer shows, they also did Images & Words in their entirety.
NIN: On what was supposedly the band's last US dates ever, they brought out Downward Spiral in its entirety. Personally, I'd rather have heard them do Pretty Hate Machine, especially for Sanctified.
Rush has never doen an album in its entirety, not even on the album's tour (aside from perhaps their early tour). However, they did bring back the song 2112 for the Test For Echoes tour, and played all of it, something I believe they never did, even on the 2112 tour. They're one band that I'd love to see do a classic album, either Permanent waves or moving Pictures (of course, they'd have to agree to bring back Camera Eye, something that they've steadfastly refused to do, despite audience demand, mostly because they had not been able to get into playing it).