Doctor Who and popular songs go together like fish fingers and custard. I've chosen some of the songs that are often associated with some of the Doctors as well as a few newer or niche songs for others. I decided on each based on vibes, lyrics, or as something I could see a fan edit made to. I also want to give a shoutout to my musically inclined husband for helping me find some of these songs.
Ninth Doctor: Shut Up and Dance by WALK THE MOON

"We were victims of the nightShut Up and Dance by WALK THE MOON
The chemical, physical kryptonite
Helpless to the bass and the fading light
Oh, we were bound to get together
Bound to get together"
Obviously inspired by this beautiful Doctor/Rose fan edit by Liisakee, I chose "Shut Up and Dance" for the Ninth Doctor. The themes of dancing, since that's a pivotal moment for this Doctor, but also of falling quickly and irrevocably in love seemed to fit him so well. I also find the line "She took my arm, I don't know how it happened" to work for both the Doctor when he first meets Rose, but also how her presence encourages him to live again.
Tenth Doctor: Saturn by Sleeping At Last

"You taught me the courage of stars before you leftSaturn by Sleeping At Last
How light carries on endlessly, even after death
With shortness of breath
You explained the infinite
And how rare and beautiful it is to even exist..."
I still go and watch Erika O'Brien's Ten/Rose video edited to "Saturn", which happens to be the perfect song for the Tenth Doctor. Filled with longing, a sense of how short time really is, and a love for the rare beauty of life, it sums up this Doctor so well for me. Also, the line "I couldn't help but ask you to say it all again" fits so well with the last few scenes of Ten and Rose's romance.
Eleventh Doctor: Geronimo by Sheppard

"Well I'm just a boyGeronimo by Sheppard
With a broken toy
All lost and coy
(At the curtains of the waterfall)
So it's here I stand
As a broken man
But I've found my friend
At the curtains of the waterfall."
Inspired by another fan edit, this one beautifully done by Snowlight Productions, I chose "Geronimo" for the Eleventh Doctor, especially since that happens to be his catchphrase. The ideas of rushing into things, finding friends, and being both a boy and a broken man are perfect for him. Also, the line about "when I lost it you held my hand" sums up the Doctor and companion relationship so well.
War Doctor: Ordinary Man by Globus and A.D.A.M.

"Fighting for the middleOrdinary Man by Globus and A.D.A.M.
Fading like a shadow in the morning
A stranger in the mirror
A twisted soul instead..."
Haunting in both its vocals and the accompanying music, "Ordinary Man" sums up the War Doctor for me perfectly - a warrior who has become so twisted he doesn't even recognize himself. I also found the line "helpless believers, children gone to waste" to evoke the feelings of the Gallifreyan tragedy and the Time War we see revealed in "The Day of the Doctor".
Twelfth Doctor: Pompeii by Bastille

"But if you close your eyesPompeii by Bastille
Does it almost feel like
Nothing changed at all?
And if you close your eyes
Does it almost feel like
You've been here before?"
Yes, we first meet Peter Capaldi in "The Fires of Pompeii" so maybe this song choice is a nod to that, but I also found "Pompeii" to have strong feelings of disaster, depression, and identity. It reminded me a lot of the Twelfth Doctor's journey with Missy and the destruction in "World Enough and Time/The Doctor Falls". The line "oh, where do we begin, the rubble or our sins?" also made me think of the confession dial and again, his efforts to rehabilitate Missy.
Thirteenth Doctor: Yellow by Jodie Whittaker

"Look at the starsYellow by Coldplay
Look how they shine for you
And everything you do
Yeah, they were all yellow..."
Since I first heard Jodie Whittaker's cover of the Coldplay song "Yellow", I've associated the song with her Doctor. The Thirteenth Doctor's era had the theme of "space for all", and I feel like the lyrics of this song and Jodie's singing it for charity embodied bringing the universe to everyone so well. I also feel that in a tragic way the line "for you I'd bleed myself dry" sums up the unforgiving nature of being the first female Doctor.
Fugitive Doctor: I Touched the Fire by Casey Breves

"I always felt that sparkI Touched the Fire by Casey Breves
I craved the mystery
I want to take my part
What only I can see
I want to take control
I want them to believe
So I faced the dark to see what I could be..."
As the first Doctor following the tragic abuse of being the Timeless Child, the Fugitive Doctor was the one to step out into adventure and take control of her own destiny. I chose "I Touched the Fire" for her, especially since she wasn't always aware of her status as a Time Lord. The line "I thought that what I had was all that I deserved, a bit of happiness, my corner of the Earth" fits her disguise as Ruth so well.
Fourteenth Doctor: Go Slowly Now, Sands of Time by Tuomas Holopainen

"Go slowly now, sands of timeGo Slowly Now, Sands of Time by Tuomas H
Still have some verses to pour
This wonder of life has led me home."
Not only is "Go Slowly Now, Sands of Time" inspired by Scotland and Scrooge McDuck, but it also references "Auld Lang Syne", the song I was originally going to choose. The Fourteenth Doctor's tenure was short but sweet as he found a sort of homecoming with Donna and her family. The themes of rest in this song fit him perfectly.
Fifteenth Doctor: Get This Party Started by Shirley Bassey

"Get this party started on a Saturday nightGet This Party Started by Shirley Bassey
Everybody's waitin' for me to arrive
Sendin' out the message to all of my friends..."
Now we come to the main reason I even wrote this article. I recently heard "Get This Party Started" for the first time, and immediately thought of the Fifteenth Doctor and the iconic scene where he's dancing in the club. The song fits with his fashionable yet mysterious and life-of-the-party vibes. I was also reminded of the dance he does in "The Robot Revolution" as he shows Belinda Chandra the TARDIS for the first time. I definitely could see an amazing fan edit of his happiest moments to this song.
These are the songs I've chosen for each of the New Who/Whoniverse Doctors. I'm sure there are others that fit them just as perfectly.
(If you're looking for a bonus song, "One More Time" by R. Armando Morabito (featuring Malukah and Tina Guo) fits River Song perfectly.)