private static int i = 0;
Are you sure that i should be static? If it's static there isn't too much sense of the Counter instance = new Counter() instance and the Next and the Reset methods also could be static.
Anyway, I'd use a longer variable name, like nextValue for better readability.
Furthermore, consider the drawbacks of the Singleton pattern:
This pattern makes unit testing far more difficult, as it introduces global state into an application.
More on Wikipedia.