FizzBuzz is a well known test to show that you can program. To be rather more exact, it is a simple test that does not tell you if you can program well, but if you cannot do FizzBuzz, you cannot program. This is a fail only kind of metric. We need this thing because sadly, we see people that fail FizzBuzz coming to interviews.
I have another test, which I feel is simpler than FizzBuzz, which can significantly reduce the field of candidates. I show them this code and ask them to analyze what is going on here:
Acceptable answers include puking, taking a few moments to breathe into a paper bag and mild to moderate professional swearing.
This is something that I actually run into (about 15 years ago, in the WebForms days) and I have used it ever since. That is a great way to measure just how much a candidate knows about the environment in which they operate.