Let's say your class will not be used in any collection ever( which is very unlikely though), it will be used in more than one place and by other developers. Any developer using your class will expect that if two instances of that class are equal based on equals method, they should produce same hashCode value. This fundamental assumption will be broken if hashCode is not overridden to be consistent with equals and that will prevent their code to function properly.
From Effective Java , 3rd Edition :
ITEM 11: ALWAYS OVERRIDE HASHCODE WHEN YOU OVERRIDE EQUALS
You must override hashCode in every class that overrides equals. If
you fail to do so, your class will violate the general contract for
hashCode, which will prevent it from functioning properly in
collections such as HashMap and HashSet. Here is the contract, adapted
from the Object specification :
• When the hashCode method is invoked on an object repeatedly during
an execution of an application, it must consistently return the same
value, provided no information used in equals comparisons is modified.
This value need not remain consistent from one execution of an
application to another.
• If two objects are equal according to the equals(Object) method,
then calling hashCode on the two objects must produce the same integer
result.
• If two objects are unequal according to the equals(Object) method,
it is not required that calling hashCode on each of the objects must
produce distinct results. However, the programmer should be aware that
producing distinct results for unequal objects may improve the
performance of hash tables.
The key provision that is violated when you fail to override hashCode
is the second one: equal objects must have equal hash codes. Two
distinct instances may be logically equal according to a class’s
equals method, but to Object’s hashCode method, they’re just two
objects with nothing much in common. Therefore, Object’s hashCode
method returns two seemingly random numbers instead of two equal
numbers as required by the contract.