I didn’t know that Cohen was still alive. That being said, I couldn’t name a single song that he wrote.
He wrote Hallelujah - also known as the Shrek song...
It’s beautiful... I’m amazed you haven’t heard it. I’ll bet you have...here’s a link:
http://www.youtube.com/watch?v=lwxsnRbz4NY
Here’s a version of Hallelujah sung by a Catholic Priest some months back that got 36 million views on YouTube...
http://www.youtube.com/watch?v=XYKwqj5QViQ