Static classes can be useful in certain situations, but there is a potential to abuse and/or overuse them, like most language features.
As Dylan Smith already mentioned, the most obvious case for using a static class is if you have a class with only static methods. There is no point in allowing developers to instantiate such a class.
The caveat is that an overabundance of static methods may itself indicate a flaw in your design strategy. I find that when you are creating a static function, its a good to ask yourself -- would it be better suited as either a) an instance method, or b) an extension method to an interface. The idea here is that object behaviors are usually associated with object state, meaning the behavior should belong to the object. By using a static function you are implying that the behavior shouldn't belong to any particular object.
Polymorphic and interface driven design are hindered by overusing static functions -- they cannot be overriden in derived classes nor can they be attached to an interface. Its usually better to have your 'helper' functions tied to an interface via an extension method such that all instances of the interface have access to that shared 'helper' functionality.
One situation where static functions are definitely useful, in my opinion, is in creating a .Create() or .New() method to implement logic for object creation, for instance when you want to proxy the object being created,
public class Foo
{
public static Foo New(string fooString)
{
ProxyGenerator generator = new ProxyGenerator();
return (Foo)generator.CreateClassProxy
(typeof(Foo), new object[] { fooString }, new Interceptor());
}
This can be used with a proxying framework (like Castle Dynamic Proxy) where you want to intercept / inject functionality into an object, based on say, certain attributes assigned to its methods. The overall idea is that you need a special constructor because technically you are creating a copy of the original instance with special added functionality.