What design patterns are used most often?

Answer 1

Singleton also can be classified as one the most popular design pattern.

Answer 2

Hey ;)
As a beginner I often used the Strategy (Procedural), Observer and State design pattern.

Obviously there are many more patterns and their use depend simply on the situation.
I don't think you will find any general stats like charts on the usage of diff. design patterns.

Just to mention some more popular patterns:
Decorator, Command, Composite, Fascade, etc.