The obvious one is Birthday by The Beatles. Others? (I have a couple of offbeat songs in mind that I will post later.)
Happy Birthday To You-Weird Al
Trip Around The Sun-Jimmy Buffet and Martina McBride
Stevie Wonder’s “Happy Birthday”.
Whenever I sing birthday greetings to my peeps who also came of age in the 80s, it’s Happy Birthday by Altered Images
Happy Birthday to You. Surprised that wasn’t mentioned earlier.
Go, shorty
It’s your birthday
We gon’ party like it’s your birthday
(50 Cent - In Da Club (Official Music Video) - YouTube)
A lot of Christmas music.
“Cindy’s Birthday” sung by Johnny Crawford.
Happy Birthday by The Birthday Party
If you’re up for a interesting birthday comedy story, I recommend Nanjiali’s “Cobra vs. Mongoose: A Birthday Party In Pakistan”. There’s nothing quite like that.