(C#) By default, I use static methods in static classes and non-static methods in non-static classes.
As I elaborate a class, I find myself naturally converging on making it entirely static or entirely non-static. Practially speaking, if I start wanting to define static members within a non-static class, I often find that it will eventually make the most sense to break those out into a separate static class -- either a utility class like Math or a global application class (like .NET's ConfigurationManager).
From an object-oriented perspective, a method is doing something to/with an object. So if you're using an instantiated object, it makes the most sense to me to think of that object's methods as non-static. Technically, you technically can make a non-static class have static members if they don't require access to an instance. But ostensibly, at least, a class's methods would still be doing something to/with that class, so I would still make them non-static. All things being equal, that is.