#Java, 130 bytes

This is for recent Java versions (7+). In older ones you can shave some more off using the enum trick, but I don't think the logic gets any shorter than this (86 inside main).

class F{public static void main(String[]a){for(int i=0;i++<100;)System.out.println((i%3<1?"Fizz":"")+(i%5<1?"Buzz":i%3<1?"":i));}}

Java, 130 bytes

This is for recent Java versions (7+). In older ones you can shave some more off using the enum trick, but I don't think the logic gets any shorter than this (86 inside main).

class F{public static void main(String[]a){for(int i=0;i++<100;)System.out.println((i%3<1?"Fizz":"")+(i%5<1?"Buzz":i%3<1?"":i));}}