you’re asking for your favorite now from that decade? if you want your favorite some from back then it would produce a different answer.
Eurythmics, “Sweet Dreams” - I’ve always thought it a remarkably apt description of the world. 
Though this actually came out eight months before I was born.
Born in the 60s - Penny Lane
“(Ya Got) Trouble”
I was born in the late 90s, and although this is kind of sad, I’m having trouble thinking of songs from then that I like - I listen to music mainly from the 60’s to the early 70’s. Maybe something by Lyle Lovett, like “If I Had a Boat”? I honestly have no idea.
1977: CB Savage, just because it’s completely insane (and hilarious!), a lot the like 70s in general.
1970s. Steve Goodman’s * City of New Orleans.*
1970s. Stevie Wonder’s “Superstition.” Although David Bowie’s “Heroes” is a close second.
1960s: ** Dear Mr. Fantasy**
or Hey Joe (Hendrix version)
https://www.youtube.com/watch?v=Zr6BBTC2so4
1958 * Make Believe* by Conway Twitty
1970s. The Clash, “Complete Control”.
1950s. Mack the Knife.
1950s. If we’re allowing instrumentals, I’d have to say Thelonious Monk’s Straight, No Chaser.
Old fart alert:
Born 1960–fave song “Puff, the Magic Dragon.”
I was born on the very day that the Beatles finished “With a Little Help From My Friends”, and the same day they shot the cover for Sgt. Pepper, so there you go. 
There’s no way I can possibly pick just one favorite from the 1960’s (born in the Summer Of '69…oh yeah).
Superstition came out while my mom was pregnant with me, and I like to think it infused me with a love of both funk and skepticism at a cellular level.
Yes, I mean it’s your favorite from that decade now. Depending on how late in the decade you were born, you might not have *had *a favorite back then. (but according to my mom my favorite 70s song during the 70s was Cher’s “Dark Lady” which is an odd choice for a 2-year-old…)
Only one! Oh, you are cruel! Well, I was torn between “Beyond the Sea” and “Mack the Knife”, both by Bobby Darin, but since I can’t decide, I will offer up “Why Do Fools Fall In Love” by Frankie Lymon and the Teenagers.
I won’t even mention “White Christmas” by the Drifters.
“Why Do Fools Fall In Love” it is!
I was born in 1962, and I have vague memories of hearing “I Want to Hold Your Hand” at a bus stop, playing on a transistor radio, when I lived in Northern Ireland.
The 1960s contained an explosion of music though, and picking one song from that decade is impossible.
I didn’t start appreciating music until I was close to my teen years, and my tastes have progressed through the decades, but “I Want to Hold Your Hand” is a song I actually remember hearing when it was popular, so I’ll go with that.