Class is an object.
But an object is not a class.

object is an instance of a class or in other words object 
is a snapshot(blueprint)of a perticuler class.
class is real world object.

Class is a user defined data type whereas Object can be 
veiwed as a variable of class type
For example fruit is a class & mango,apple are different 
objects of class fruit.
Class can be a person whereas objects can be any existing 
person like Ram ,Shayam,Rahul etc

a class is a class which is an object but class is not an 
object

Yes, class is an object but an object is not a class.
We can compare class with a factory and object with product.
A factory can be a product of another factory; but a 
product can not be a factory.

A class is a generalized template from which object
is created based on its various instances,therefore
we can consider a class as an object while vice-versa 
is not possible.

A class is neither an object nor an object is a class.
A class is like a blue print for an object.
An object is an instance of a class.

Some people have given the right examples above and some 
more goes here:
You can consider a blue print for your house is a class. 
You cannot stay in blue print :).
The building built based on the blue print is called an 
object. You can stay in it.

Class should be treated like a "data type" and an object 
like a instance of that datatype.
for e.g., int i; you can considet int as a class and i as 
an instance of an object.

YES class is an object whereas an object is an instance of 
a class

Class is not an object. An object is an entity that is 
allocated memory during runtime to do certain operation 
whereas Class is just a skeleton or representation of the 
object. We say design a class and not create a class. We 
can only design a class ( attributes and behaviour ).
In brief we can say class is a Type of an object.

Going by the definition ("object is an instance of a class") -  it is clear that object IS A class type (take off "an instance of"). However, the other way round is against the correctness of definition.