So Here We Are - Bloc Party
Jungle Love
I am for you by Lisa tucker
wild horses by The Sundays
Killer by Kate York
Well, for Season 5, the ending song was "As Tears Go By" by the Rolling Stones.
The song is Fields of Gold by Eva Cassidy. I hope this helped.
Passing afternoon, by Iron and Wine
"God's Gonna Cut You Down"
Any other world - Mika
it's Friend Like You by Joshua Radin
One was Sail by awolnation another was All I Need by the same band/singer.
Season Three of Burn Notice just started on June 4th, so the finale hasn't happened yet, but for the finale of season two, the song playing when he jumps out of the helicopter is "Time Bomb" by Jessy Greene.