Here is a very interesting formula for pi, discovered by David Bailey, Peter Borwein, and Simon Plouffe in 1995:
Pi = SUMk=0 to infinity 16-k [ 4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6) ].
The reason this pi formula is so interesting is because it can be used to calculate the N-th digit of Pi (in base 16) without having to calculate all of the previous digits!
Examples computer programs
To see Pi to 1000,000 decimal digits use the PiDay site