The first Pi Day was celebrated in 1988, when it was created by Larry Shaw, a San Francisco Exploratorium physicist. For that first Pi Day, both staff and visitors marched around one of the Exploratorium's circular spaces, then followed that up with a feast of fruit pies. The Exploratorium continues to hold Pi Day celebrations, and has a page dedicated to today's event, as well.
The Exploratorium will have a live webcast on explo.tv (beginning at 1:00 p.m. PDT); they will also be making their presence known in the virtual world, Second Life.
For those who want to be "more significant" in terms of digits, Wikipedia says that some are calling March 14th, 2015 at 9:26:53 a.m. as "Real Pi Day." These numbers for the date and the time combined (3/14/15, 9:26:53) correspond to the first 10 digits of pi (3.141592653).
On March 12, 2009, the U.S. House of Representatives passed a non-binding resolution (HRES 224), which recognized March 14, 2009, as National Pi Day. Meanwhile, on Pi Day 2010, Google used one of its familiar Google Doodles to celebrate the faux holiday.
Pi has often been (over)used in science fiction to "disarm" rogue computers and robots. The frequently used request is to ask the offending automaton to recite pi to the final digit, resulting in a robotic form of a nervous breakdown. You can watch Spock turn a computer into mush in a Star Trek clip, below.
Sadly, it doesn't appear restaurants like Baker's Square or Marie Callender's will be celebrating Pi Day. After all, there was already a National Pie Day (with an e) earlier this year.