Sgt Pepper's.
Ok, it is perhaps a throw away suggestion at first glance but My dad and I listened to it from when I was three or four on a Sunday morning (along with other albums) and it has remained one of my favourite albums. It has a good mix of McCartneys 'Granny S**t Music' as Lennon described it, but also has proto rock tracks (Sgt Pepper's Lonely Hearts club band) as well as slightly more blue and deep tracks plus two heart tuggers in She's leaving home and Day in the life.
Over all a beautiful album both audio and visual.
As a contender for a modern classic album: Super Grass by Super Grass released in 1999. I liked their earlier rock-punk nodding albums 'I should Coco' and 'In it for the money', but with 'Supergrass' they started exploring music further, and it has it's funny moments like the other two albums including 'Lord came from outta space'.
Garbage's self titled first album.
Led Zep I-IV, Physical Graffiti and Presence.
Travis 'The man who' (Gorgeous album)
The Shins 'Wincing the night away' and 'Chutes too narrow'
I have listened to 6 Music for about five years now and don't regret a moment of it.