I always liked the version with no branching statements. In python it would be roughly:

    def fizz_str(n):
        return "FIZZ"


    def buzz_str(n):
        return "BUZZ"


    def fizz_buzz_str(n):
        return "FIZZBUZZ"


    def to_str(n):
        return str(n)


    indexes = [3, 0, 0, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 0, 0]


    def fizz_buzz(n):
        funcs = [
            to_str,
            fizz_str,
            buzz_str,
            fizz_buzz_str
        ]
        return funcs[indexes[n % 15]](n)


    for i in range(1, 101):
        print(fizz_buzz(i))