Two of the songs from their latest album "Saturday Nights and Sunday Mornings" can be downloaded from HERE. Totally legit from Countingcrows.com and totally free.
The two tracks are "1492" and "When I Dream of Michelangelo." They are downloadable together in a convenient .zip file that just needs to be extracted. I've only listened to them all the way through once, and I think I prefer the second tune. I really like a lot of their previous stuff and I feel like "1492" is a little less soulful than I've come to expect. Whatever your feelings, if you like Counting Crows (you HAVE to love free legal music downloads from prominent bands) then you should check this out; don't know how long they'll be available for download, so hop to it, and ENJOY!