I don’t get it. 
3.141592.
I’ve had 3.14159 memorized since grade school. The two I remember, because it’s the first number after the section that I remember.
It makes sense to me, okay?
I voted 13, but really know 17, which is how many you ever need for double precision floating point numbers.
ETA: How does someone know two digits? 3.1? How will you know when to eat pie?
3.1415926535897932384626433832795
EDIT: I learned them by memorizing them to a rhythm in my head.
Can I have a large container of coffee? Thank you.
30 decimal places - about one inch error in the light-year.
[spoiler]Now I - even I - would celebrate
In rhymes unapt the great
Immortal Syracusan rivaled nevermore
Who in his wondrous lore
Passed on before
Gave men his guidance how to circles mensurate.
3.141592653589793238462643383279[/spoiler]
I voted 20+, but only because of the poem:
Now, I will a rhyme construct
By chosen words the young instruct
Cunningly devised endeavour
Con it and remember ever
Widths in circles here you see
Stretched out in strange infinity
When I was in Jr. High, I memorized it to 50 places, so I think I can remember it to at least 20 places. The spaces are the pauses in my memorization scheme.
3.14159 2 653 589 793 238 46264 338 327 950 and then it gets fuzzy. How’d I do?
I am familiar with all ten.
But, as for how far I remember the expansion… uh, 3.14159. I guess that counts as six? (Of course, I could sit down with pen and paper and slowly calculate as many more as I wanted…) That’s already way more than anyone needs to memorize for anything, as far as I’m concerned. (Besides, it’s 2*pi that’s really the more fundamental constant, IMHO, making all the fetishization pi receives particularly silly…)
Edit: The poll lacks an option for six, for some reason, and on reflection I decided you probably wanted to count this as five, anyway, so I went with that
7
3.141592
Which I guess introduces a small rounding error. 
20+. I can remember 3.1415926 easily enough, and from there I remember the next couple of palindromic triplets (with a spare 8 stuck in) - 535 8 979 323.
I can probably continue that most of the time - another spare 8, and then a five-digit palindrome (46264), then a 3 and another triplet (383) but at that point I’m already well past my apathy threshold.
Same here, from (I read in a Sports Illustrated article) the MIT football cheer.
And the other cheer they do when their opponents score -
The print version of the article had a picture of a player icing his knee while reading Advanced Linear Algebra.
Regards,
Shodan
I know it to 12 digits: one more and i would have looked much better in your poll!
Once upon a time when I was young and bold I memorized the first 101 decimal places of pi and could recite them in under 30 seconds. Now in my dotage I remember only the first 25.
I only know it to 3.14159 because there’s a fairly well-known riddle in which you ask someone what the next number in the series is and give them 3, 1, 4, 1, and 5.
BTW, I’m assuming by “digits” the poll meant, “digits to the right of the decimal place.” Was that correct?
I know it to 101 decimals. I memorized it while on the long drive back from a vacation when I was 15. It serves as a great ice breaker.
So here we go:
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798
Would you like me to fix your mouse-over problem?
I was taught the “May I have a large container of coffee” rule for the first 8 places.
For e, a professor taught us how to remember 2.718281828459045 like this:
2.7 you have to memorize
in 1828 Andrew Jackson was elected for the first of two terms so you get 18281828
459045 is the well known right isosceles triange.
Please explain to this loser how the rhymes/poems/etc. provide meaning. Thanks.
I thought it was 3.141592653588. I’m so ashamed.
Mine? Count the letters in each word. (I have to remember to spell “rivaled” the American way - in English it takes a double l.)
Oh, and the error is nothing like an inch in the light-year - I was thinking a light-year was 6 * 10[sup]24[/sup] miles, it’s only 6 * 10[sup]12[/sup]. That make the accuracy of pi to 30 places more like a millionth of an inch in the distance from here to the Andromeda Galaxy.