"Blue Lips" - Regina Spektor (Regina is fantastic if you've never heard her)
"Blue Angel" - Antony and the Johnsons (another lesser known but AMAZING artist)
"Niger Blues" - Ludovico Einaudi (instrumental - Einaudi, I think, is one of the greatest composers alive today)
"Age Old Blue" - Alela Diane (Oh, man! another great one - folksy)
"Blue" (Ba Da Bee) - Eiffel 65 (dance)
And then of course a few more classics not mentioned yet.
"Blue" - Jayhawks (always liked this one)
"Blue Sky Mine" - Midnight Oil (can we call them classic yet?)
"Blueberry Hill" - Fats Domino (hard to go wrong with Fats)
"Blue Skies" - Irving Berlin (sung by just about everyone - I kind of like Eva Cassidy's version).
"Song Sung Blue" + "Forever in Blue Jeans" - Neil Diamond
"California Blue" + "Blue Angel" - Roy Orbison