Probably not the "best" but some of my favorites:
Rilo Kiley "The Execution of All Things"
The Elected "Sun, Sun, Sun"
Tilly and the Wall "Bottoms of Barrels"
Wilco "Yankee Hotel Foxtrot"
Tegan and Sara "The Con"
The Decemberists "Picaresque"
The Postal Service "Give Up"
And I have to give a special shout-out to "War of Women" by Joe Firstman. It's not my favorite of his work, and it's definitely not the best album of the aughts, but it has deep sentimental value and not including it just feels wrong.
Immediately afterwards I realized I left out "I'm Wide Awake, It's Morning" by Bright Eyes, and I've thought of a few others since then. And would you believe that I'm the only person so far that chose "The Execution of All Things" as the best RK album? Everyone else chose "More Adventurous." I think when the final list is composed, the only albums I chose that will make the cut will be "Yankee Hotel Foxtrot" and "Give Up." Maybe "Picaresque" but the Decemberists votes seem to be split between "Picaresque" and "Castaways and Cutouts." That could hurt the Decemberists' chances of making the list at all.