There are some classes which can be instantiated only by calling static methods (example ResourceBundle). But even these methods will internally call the constructors and return a reference to the newly instantiated object.
If you're interested in yourself creating an instance without calling a constructor: you won't be able to do it.
If you're wondering if an instance can come into being without a constructor being called: yes, there are several ways. The default clone() implementation doesn't call the class's constructor; neither does the serialization machinery when an object is deserialized.
You are not supposed to write a constructor for each class. But a default constructor method (without any parameter) exists in class definiton. Also, writing constructor will give you opportunity to configure your class. (like constraints in some parameters).
On the other hand, for static classes, you do not need to use construct method as others say.