Quick! Name two songs that have a phone number in their title! If this isn't your first choice, I'm sorely disappointed. (I'd accept any number of songs, including "Pennsylvania 6-5000" or Squeeze's "853-5937" for the second).
A song that is referred to in pop culture possibly more than any other in history, Tommy Tutone - it was the name of the band, led by Tommy Heath - performed a power-pop gem in the early 80's. A desperate tale of misguided, unrequited love, it was loosely based on a real person known by the band!
Here's a little trick you can do with this number. A lot of stores - grocery and otherwise - have loyalty cards or discount programs that come with a card. If you don't have the card, usually this can be searched by telephone number. 867-5309 works in almost every area code.
Here's a little trick Tommy Heath did with the tune in 2008 with an acoustic guitar.
Here's the mathematical representation of Jenny's Constant according to xkcd. Incidentally, 8,675,309 is a prime number. Not only was it a one-hit wonder, it's a mathematical anomaly!