Like Geddy, Sting and Jeff Buckley are likely to set me off.
Most notably, Sting's Fragile - both before and after 9/11,
Shape of My Heart,
and Fortress Around Your Heart.
Jeff Buckley's Mojo Pin (live version from "Live at Sin-e" especially),
Corpus Christi Carol,
and Halleluljah are also usually guaranteed to launch me into floods of tears.
Neil Finn's Turn and Run, which Heidi mentioned, also does it for me.
Into the Sunset is another one which I can't listen to right now without stifling a sob...
Crowded House have a few tear-jerkers also:
Walking on the Spot,
Whispers and Moans,
Split Enz's Years Go By will get me every time, and always has.
I Hope I Never usually gets the tears flowing as well.
I think I'll stop there for now...