For years, both Superman's age and birthdate have been variable in the comics, but the most consistently-used birthday for Superman is February 29. The in-real-life joke is that since Superman never seems to age, it makes sense that he has a birthday that only comes around once every four years. In the comics, there was at one point a similar logic that held Krypton's year was significantly longer than Earth's.
Clark Kent, meanwhile, will celebrate his birthday on June 18, the date the Kents first found the rocket. June 18 is also the birthdate of Superman voice actor Bud Collyer, who played the first live-action Superman.
In 1985, one of the best-loved Superman stories of all time was published: "For the Man Who Has Everything," published in Superman Annual #11 by the Watchmen creative team of Alan Moore and Dave Gibbons, took place on Superman's birthday. That story was adapted into an episode of Justice League Unlimited, and was the basis for a recent episode of Supergirl.
You can buy it digitally here.
As an aside, today is also the birthday of Michael Bailey, Superman super-fan and co-host of From Crisis to Crisis: A Superman Podcast. Just don't ask him to take his glasses off.