I might as well weigh in with this, there's probably glaring emissions, which is due to picking the first ten that sprang to mind, and keeping that order too:
1. KC Rules OK - King Creosote
2. Person Pitch - Panda Bear
3. Passover - The Black Angels
4. Original Pirate Material - The Streets
5. Elephant - The White Stripes
6. A Brighter Beat - Malcolm Middleton
7. Midnight Organ Fight - Frightened Rabbit
8. Alas I Cannot Swim - Laura Marling
9. Get Yr Blood Sucked Out - Viva Voce
10. Walking With Thee - Clinic
If you have Spotify, I've made a playlist, which can be accessed here.
I wonder if there'd be any consensus if we picked the best album of the noughties in these here comments.....