The pi birthday exists in the same vein as the "half birthday"; an
essentially purposeless occasion that serves only as an excuse
to
celebrate.

Pi birthdays are usually celebrated only twice in the course of
one's life. The first is when you're 3.14159265 years old. As most
people are unable
to party for themselves at this age, the
event
serves as a cute mathematically-themed photo-op for the
family
album.

When a person is 31.41592653 years old, they can throw
themselves a fun, themed get-together to celebrate their
second
pi birthday. Friends are encouraged to bring circular gifts. Pie is
enjoyed by all. Endurance recitation contests are held and
celebrators are encouraged to do things irrationally.

In the future, a third pi birthday may be celebrated at age
314.15926535. I have no doubt that it will be an equally festive
occasion.

Oh yes, definitely. But strictly speaking it would
occur at an unknown instant so finely defined that
special relativity would make it different for each
person and different parts of the same person.

For myself, i'll be pi times a dozen and two about a
week before my forty-fourth birthday. Makes me
wonder how close it gets to whole years in
someone's lifetime.

Exponential birthday intervals make sense because
time speeds up as you get older, but slicing pi (ooh!)
decimally like that is too much of a concession to
base ten for me.

There may be many transcendentals, but only a few have names. I especially like Chaitin Day, which is transcendental, yet unknown and unknowable. (More like a death day.)

Having missed the only two Pi Birthdays that I'm ever likely to have, I'd like to propose birthdays based on the first Feigenbaum constant instead, so I've still got one to look forward to.

I'm all for celebrating every (named) transcendental
number. And if it's too difficult to exactly place the
instant of the pi birthday, I think it would be
acceptable to use 22/7 as a replacement.

Yes, but so would everyone else. Assuming you only
remembered a finite number of your friends'
birthdays you would therefore fail to remember an
infinite number of your friends' birthdays. The ratio
of remembered birthdays to forgotten birthdays
would thus be zero, and none of your friends would
like you any more.

I don't think that's a problem. People generally don't try to remember their friends' birthdays with infinite accuracy; identifying the date alone is fine. So there's no remembering needed, because you know by definition that each of your friends has uncountably many birthdays every day.

Birthdays are already set up based on pi: one year is an orbit, or a complete circle around the sun. However, the circle is not a very engineeringly accepted unit - it should be considered to be 2*pi AU.
So it would make more sense from an engineering standpoint to have a birthday (AU day? Radian day?) every 12/(2*pi) months.

(Or 365.24/(2*pi) days = about every 58 days, 3 hrs, 7 minutes. (Rounded up 'cause most alarms don't do seconds.))

It's not a circle though. Pi presumably comes into it at some point but this planet's orbit has an eccentricity of roughly one five-dozenth, and it varies in speed so it would cover the same angular distance variably (hence the Martian Rotterdam month-naming system, since on Mars the issue is more severe). Also, there are several different kinds of year, for instance tropical and sidereal.

That's both neat and true, [lurch]. My personal preference would be to celebrate one's birthday according to the orbit of the planet governing one's sun sign.

A close member of my family has her birthday on pi day: 14 of
March, and in 2015 it had two extra digits to it. 3.14.15

Vi Hart has some videos extensively attacking pi and
proposing the representation of a full circle instead, called
Tau. (Her birthday is on the 28th of June... and her chosen
name rhymes with pi...)