(I think) my favourite album of the 00s and (so far) of this decade are Forever Emma by Bon Iver and Eliminator by Ty Segall. I'm not so sure they've been mentioned on this thread, but both deserve a go.
There are two cracking albums on this list.
On a different note, Sgt Peppers probably is the complete album, but it's nowhere near as good as Abbey Road in my book which is marred by Maxwell's Silver Hammer and Octopus' Garden. Closer and Unknown Pleasures are both right up there for me too...