Sum of Fibonacci numbers -- speed contest
Python, 7 chars

It turns out that the period of G(i)=F(i) mod 10^9 is 1.5e9 exactly.  So when adding them up, we can group them into groups of size 1.5e9, each of which will have the same sum (mod 10^9).  Turns out, that sum is 0.  So if we take N to be any multiple of 1.5e9, the sum of the first N fibonacci numbers is 0.  So:

print 0


will, given an argument i, print the sum of the first i * 1.5e9 Fibonacci numbers.  Super fast and works for an arbitrarily large i.