Here is summary of what I have written so far on singleton patterns. The examples taken here are mostly from Java.

Singleton Pattern #1: Basics, Definition, Usage
Gives a basic idea of singleton pattern is all about.

Singleton Pattern #2: Lazy vs Eager Instantiation for a Singleton Class
The difference between two types of instantiations, and which one is better under what circumstances.

Singleton Pattern #3: Problems with Singleton, Thread-Safe Singleton Class
Issues with using singleton, how to make your singleton classes threadsafe.

Singleton Pattern #4: Difference between Singleton and Static classes
Sometimes people confuse between singleton and static classes. When should one use them and why?