Isn't the music the most important part of an ad? It can make you love one for no apparent reason and you will probably remember that song forever.
Here are some ads with great music that I gathered. Some are recent and others were on TV more than 10 years ago. Hope you like them and get to know a few great songs if you didn't know them already!
(I'm from Spain, so some of the ads were only broadcasted in my country, but they're cool and the songs are still superb anyway).

I'm A Terrible Person, by Rooney (Carolina Herrera, 2009)

cacti, pink, and cactus image red, girl, and art image
Ad: Song not on Spotify :( YouTube:

Only Man, by Audio Bullys (Cornetto, 2011)

site models, love+tumblr+instagram, and giant teddy bear image love, couple, and goals image
Ad: Song:

Jungle Drum, by Emilíana Torrini (El Corte Inglés, 2014)

rptheme and random theme image outfit, aesthetic, and style image
Ad: Song:

Pumpin Blood, by NONONO (Deichmann, 2013)

Image by sa0a0 blue, jeans, and outfit image
Ad: Song:

Aventura, by Mavi Phoenix (Desigual, 2017)

adidas, aventura, and Barcelona image adidas, aventura, and Barcelona image
Ad: Song:

Heavy Cross, by Gossip (Dior, 2013)

glitter, gold, and aesthetic image bonfire night, fire, and fireworks image
Ad: Song:

She's A Lady, by LION BABE (H&M, 2016)

krysten ritter image art, glam, and beauty image
Ad: Song:

WHAM RAP! (Enjoy What You Do?), by Wham! (H&M, 2017)

yellow, aesthetic, and guitar image yellow, flowers, and aesthetic image
Ad: Song:

Out Of It, by Fallulah (Opticalia, 2015)

pink, phone, and aesthetic image pink, heart, and wallpaper image
Ad: Song:

On Our Way, The Royal Concept (Orange, 2014)

aesthetic, orange, and water image balloon, bubble, and orange image
Ad: Song:
Cover image from @xndrexqt:
aesthetic, barbie, and creepy image