Here's one I did a while ago with U2 songs:
Endless Deep - Lillith
Magnificent - Merlin
The Fool - Folly
Do You Feel Loved - Mug the gargoyle
Where Did It All Go Wrong? - Jamie (Series 2)
Disappearing Act - Steven (Series 2)
Out Of Control - Mildread on her broomstick
Stand Up Comedy - Motley
A Man And A Woman - Mrs Grimwold
Stay - Festus
I Fall Down - Mellisandre
One Step Closer - Scott (Series 3)
So Cruel - Morghanna
One - Hordriss
Shadows And Tall Trees - Oakley
Big Girls Are Best - Gundrada
Exit - Doorkis
Silver And Gold - the Boatman
I Still Haven't Found What I'm Looking For - Malice
Christmas (Baby Please Come Home) - Giles (Series 4)
Winter - Aesandre
The Wanderer - Ridolfo
Pride - Greystagg
The Ocean - Captain Nemanor
Scarlet - Red Death
Stranger In A Strange Land - Grimaldine
Mysterious Ways - Brother Strange
I Will Follow - the Grayling
An Cat Dubh - Bethsemane
Crumbs From Your Table - Ben (Series 7)
Bad - Lord Fear
Surrender (or Moment Of Surrender) - NOT Lord Fear
Your Blue Room - Tim Child
David also suggested Wild Honey - Skarkill, and Stuck In A Moment You Can't Get Out Of - Stuart (Series 2)!

And here's my attempt with songs by The Waterboys:
The Dance At The Crossroads (or Always Dancing, Never Getting Tired) - McGrew
Peace Of Iona - Greystagg
I've Lived Here Before - Treguard of Dunshelm
His Word Is Not His Bond - Honesty Bartram
Malediction - Maldame
Strange Boat - the Boatman
Fisherman's Blues - Ridolfo
We Will Not Be Lovers - any dungeon female to Motley
It Should Have Been You - Leo, Sophia, Nathan etc...
I Will Not Follow - Cedric in Ariadne's lair
This Old Ship (or This Is The Sea) - Captain Nemanor
One Sweet Step At A Time - dungeoneers in Merlin's throne room
My Dark Side - Mogdred
Questions - the Brollachan, or any wall monster
One Of Many Rescuers - anyone who saves Romahna
Open - the weeping doors
Preparing To Fly - Smirkenorff
Winter Winter - Aesandre
Be My Enemy - Lord Fear
Wonderful Disguise - Hordriss
Everybody Takes A Tumble - Lillith