Those Were the Days- Mary Hopkin
You've got to see this version too! Leningrad Cowboys rock.
Two Little Boys- Rolf Harris
Sinead does a touching a capella version too...
Zombie- The Cranberries
One Tin Soldier- The Original Caste
Runaway Train- Soul Asylum
Hazard- Richard Marx (embedding not permitted for the actual music video, so it's one of those annoying youtube montages...)
Theme from Dot and the Kangaroo (STILL makes me tear up)
99 Red Balloons- Nena
Screaming at the Wailing Wall- Flogging Molly
Rainbow Connection- Jim Henson
Fast Car- Tracy Chapman (and this isn't even the song she wrote about a guy beating his woman to death...)