SimsDomination has an incomplete list of songs that will be included with Pets.

UPDATE: I’ve added YouTube links to most of the songs.

The Sims 3 Pets Soundtrack / The Sims 3 Pets Soundtrack
Alex Boyd – Light Up Tonight
Cher Lloyd – Superhero
Erasure – Where I Start To (Break It All Down)
Kimbra – Good Intent
Anjulie – Headphones
Asher Roth – Another One Down
BG5 – Lay A Little Sunshine
Blush – Undivided
CSS – City Grrrl
Earnhardt Jr. Dale Jr – Morning Thought
Jack’s Mannequin – Television
Joshua Radin – Here Lies
Katy Rose – A Part Of It
Lenka – Two
Luke Bryan – Country Girl (Shake It For Me)
Martina McBride – Teenage Daughters
Mona – Lean Into The Fall
Outasight – Life Or Something Like It
Robby Armstrong – Rodeo
Rock Mafia – The Big Bang
Speakers – Gimme Go
The KickDrums – Counting On You
The Lunabelles – A Place To Shine
Thompson Square – I Got You
Wolf Gang – The King And All Of His Men
Carpool – Shine On
Fall On Your Sword – New Ways to Vandalize Your Heart
Galactic – Ohhh Ahhh

This list can be found in the credits of the Create A Pet demo.

Thanks to Felipe of Os Games EA for the tip!