52 chars in Python:
print 4*sum(((-1.)**i/(2*i+1)for i in xrange(5**8)))
(51 dropping the 'x' from xrange.)
36 chars in Octave (or Matlab):
l=0:5^8;disp((-1).^l*(4./(2.*l+1))')
(execute "format long;" to show all the significant digits.) Omitting 'disp' we reach 30 chars:
octave:5> l=0:5^8;(-1).^l*(4./(2.*l+1))'
ans = 3.14159009359631
