A static class cannot contain any constructors, only a static constructor that is called first time one of its members is accessed.
That is basically the difference. Performance wise we also get another for free by the compiler since it can check to make sure that no instance members are accidentally added. The compiler will guarantee that instances of this class cannot be created.
Static classes are also sealed and therefore cannot be inherited.
http://msdn.microsoft.com/en-us/library/79b3xss3(v=VS.100).aspx
A static class is basically the same as a non-static class, but there is one difference: a static class cannot be instantiated. In other words, you cannot use the new keyword to create a variable of the class type.
Another valid point is that Extension Methods has to be declared in a static class
http://en.wikipedia.org/wiki/Extension_method
The new language feature of extension methods in C# 3.0, however, makes the latter code possible. This approach requires a static class and a static method.