Haskell
I got it down to 34 characters:
foldl subtract 4$map(4/)[3,5..9^6]
This expression yields 3.141596416935556 when evaluated.
Edit: here's a somewhat shorter version (at 33 characters) that uses foldl1 instead of foldl:
foldl1 subtract$map(4/)[1,3..9^6]
Edit 2: 9^6 instead of 10^6. One has to be economical ;)
Edit 3: Replaced with foldl' and foldl1' with foldl and foldl1 respectively—as a result of Edit 2, it no longer overflows. Thanks to ShreevatsaR for noticing this.