What does this option do?

The JSHint eqeqeq option is used to prohibit the use of the equals operator == and the does-not-equal operator !=. This enforces the use of the strict equality operators (=== and !== instead). The strict equality operators differ from their non-strict counterparts by first comparing the type of each operand, rather than attempting to coerce them to a common type. In the following example we make use of the non-strict equality operator to check whether a value is either null or undefined:

/*jshint eqeqeq: true */
var x;
if (x == null) {
    // This will execute if x is null or undefined
    doSomething();
}

When should I use this option?

The use of the eqeqeq JSHint option will cause an "Expected '===' and instead saw '=='" error any time it encounters an equals or does-not-equal operator. As demonstrated in the above example these operators can be used in some situations to produce shorter code. However, their use can lead to bugs and unexpected behaviour. For that reason it's generally considered best practice to use the strict equality operators wherever possible. The example above can be written as follows instead:

/*jshint eqeqeq: true */
var x;
if (typeof x === "undefined" || x === null) {
    // This will execute if x is null or undefined
    doSomething();
}

Note that this is an enforcing option which means JSHint does not apply it by default. If you do not explicitly set this option to true JSHint will allow the use of non-strict equality operators anywhere in your code.

Recommendation

Set this option to true (enforces the use of strict equality operators).