Joshua Bloch says on Effective Java

You must override hashCode() in every class that overrides equals(). Failure to do so will result in a violation of the general contract for Object.hashCode(), which will prevent your class from functioning properly in conjunction with all hash-based collections, including HashMap, HashSet, and Hashtable.

Let's try to understand it with an example of what would happen if we override equals() without overriding hashCode() and attempt to use a Map.

Say we have a class like this and that two objects of MyClass are equal if their importantField is equal (with hashCode() and equals() generated by eclipse)

public class MyClass {
    private final String importantField;
    private final String anotherField;

    public MyClass(final String equalField, final String anotherField) {
        this.importantField = equalField;
        this.anotherField = anotherField;
    }

    @Override
    public int hashCode() {
        final int prime = 31;
        int result = 1;
        result = prime * result
                + ((importantField == null) ? 0 : importantField.hashCode());
        return result;
    }

    @Override
    public boolean equals(final Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        final MyClass other = (MyClass) obj;
        if (importantField == null) {
            if (other.importantField != null)
                return false;
        } else if (!importantField.equals(other.importantField))
            return false;
        return true;
    }
}

Imagine you have this

MyClass first = new MyClass("a","first");
MyClass second = new MyClass("a","second");

Override only equals

If only equals is overriden, then when you call myMap.put(first,someValue) first will hash to some bucket and when you call myMap.put(second,someOtherValue) it will hash to some other bucket (as they have a different hashCode). So, although they are equal, as they don't hash to the same bucket, the map can't realize it and both of them stay in the map.

Although it is not necessary to override equals() if we override hashCode(), let's see what would happen in this particular case where we know that two objects of MyClass are equal if their importantField is equal but we do not override equals().

Override only hashCode

If you only override hashCode then when you call myMap.put(first,someValue) it takes first, calculates its hashCode and stores it in a given bucket. Then when you call myMap.put(second,someOtherValue) it should replace first with second as per the Map Documentation because they are equal (according to the business requirement).

But the problem is that equals was not redefined, so when the map hashes second and iterates through the bucket looking if there is an object k such that second.equals(k) is true it won't find any as second.equals(first) will be false.

Hope it was clear