I'll start, one song that reminds me of D/R is:
Open Your Eyes - Snow Patrol

This has nothing to do with anything really, but I've always thought that Owl Citys songs are very Dr Who, and even the lyrics fit some of the episode PERFECTLY!

Run by Snow Patrol. Can;t think of any more right now, but Dog Dayz by Florence the Machine reminds me of Doctor Who in general.

What I wanted to say by Colbie Caillat.
many more, too.

Vanilla Twilight, Owl city. :)

Mad World. Never did before but I just watched a brilliant fan video, and now I know I will always think of them when I hear it. And that random one by Glen Miller -- becuase the doctor dances to it in The Doctor Dances! :D :D I also always cry when I hear murray gold's "Doomsday"...

"Slipped Away" by Avril Lavigne.
"Drops of Jupiter" by Train.

Enchanted by Taylor Swift
Innocent by Taylor Swift
Invisible by Taylor Swift
Our Kind of Love by Lady Antebellum
Pretending by the Glee Cast
Quitter by carrie Underwood
Ready to Love Again by Lady Antebellum
Superman by Taylor Swift
Tied Together With A Smile by Taylor Swift
Beautiful Disaster by Kelly Clarkson
Trying Not To Love You by Nickelback
Don't Let It End by Nickelback
When you're Gone by Avril Lavigne
Wish You Were Here by Avril Lavigne
My Immortal by Evanescence
You Found Me by Kelly Clarkson
A Thousand Miles by Vanessa Carlton
A Thousand Years by Christina Perri
Payphone by Maroon 5
Dark Side by Kelly Clarkson
Taking Chances by Celine Dion
Breaking Your Own Heart by Kelly Clarkson
What Hurts the Most by rascal Flatts

okay. I'm done with my mile long list, hope I've at least helped out somebody.

Boats and Birds - Gregory and the Hawk
Kaleidoscope Eyes - Panic! At The Disco
Truly Madly Deeply - One Direction

My favorites are..
Who Knew - Pink
You Found Me - The Fray

Let her go- passenger

A Thousand Years- Christina Perri, Let Her Go- Passenger, Stay Stay Stay- Taylor Swift, High- James Blunt, etc....

Shut up and dance by Walk the Moon. Especially for ''The Doctor Dances'' episode. :)

Wings by Birdy. Especially when you're an emotional mess after Doomsday