Large-scale celebration of Pi Day began in 1988, mostly through the efforts of physicists Larry Shaw and Ron Hipschmann at the San Francisco Exploratorium. The Exploratorium still runs Pi Day events 25 years later, including Pi-themed processions and pie for dessert. In 2009, Pi Day became semi-official through a vote by the House of Representatives. (They did a better job with Pi than did Indiana, who almost legislated it to be 3.2.)
The best way to celebrate Pi Day is to get together with some friends and talk math over a pie. You could even go for a pizza pie, since a pizza with radius 'z' and height 'a' has volume = pi * z * z * a. If you're too busy, there are plenty of Pi Day events to check out on the Internet, too. Princeton is holding a video contest to celebrate the day, or you can check out the pi pies people are making. If you'd care for a game, head over to the Pi Day Challenge, which features a series of pi-related logic puzzles. Or just spend the day learning about pi.
Cool pi facts: Pi is currently known to about 10 billion decimal places. You can calculate pi using the Fibonacci sequence. A few years ago, Steven Rochen mapped the digits of pi to musical notes and turned it into a violin solo (video). Others have made music from pi as well. Mankind didn't know the first hundred digits of pi until the year 1701. How many digits of pi can you recite? The record for memorization currently stands at 67890 digits. The record for reciting pi while juggling three balls is just under 10,000.