@TomaszS: So, the way I look at classes is that there are two main types of classes:
There are "domain" / model / entity classes ... classes that have state (properties) and are vital to the business problem you're trying to solve. Their methods generally act on their own object instance.
Then there are utility classes that have no state, and play a supporting role. Factories, managers, orchestrators, facades. The methods act on instances of other classes (not themselves, because, again, they have no state).
Domain classes are generally not static. Factories, managers, orchestrators ... the generally ARE static