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In 2017, I think this is the best way; that supports IE9+ and modern browsers.

function CustomError(message) {
    Object.defineProperty(this, 'name', {
        enumerable: false,
        writable: false,
        value: 'CustomError'
    });

    Object.defineProperty(this, 'message', {
        enumerable: false,
        writable: true,
        value: message
    });

    if (Error.hasOwnProperty('captureStackTrace')) { // V8
        Error.captureStackTrace(this, CustomError);
    } else {
        Object.defineProperty(this, 'stack', {
            enumerable: false,
            writable: false,
            value: (new Error(message)).stack
        });
    }
}

if (typeof Object.setPrototypeOf === 'function') {
    Object.setPrototypeOf(CustomError.prototype, Error.prototype);
} else {
    CustomError.prototype = Object.create(Error.prototype, {
        constructor: { value: CustomError }
    });
}

Also beware that __proto__ property is deprecated which is widely used in other answers.

Note: See discussion in the comments and @MattBrowne's gist.

UPDATE: Added constructor assignment. See this test for comparison on different implementations. Test module here.

In 2018, I think this is the best way; that supports IE9+ and modern browsers.

UPDATE: See this test and repo for comparison on different implementations.

function CustomError(message) {
    Object.defineProperty(this, 'name', {
        enumerable: false,
        writable: false,
        value: 'CustomError'
    });

    Object.defineProperty(this, 'message', {
        enumerable: false,
        writable: true,
        value: message
    });

    if (Error.hasOwnProperty('captureStackTrace')) { // V8
        Error.captureStackTrace(this, CustomError);
    } else {
        Object.defineProperty(this, 'stack', {
            enumerable: false,
            writable: false,
            value: (new Error(message)).stack
        });
    }
}

if (typeof Object.setPrototypeOf === 'function') {
    Object.setPrototypeOf(CustomError.prototype, Error.prototype);
} else {
    CustomError.prototype = Object.create(Error.prototype, {
        constructor: { value: CustomError }
    });
}

Also beware that __proto__ property is deprecated which is widely used in other answers.

In 2016, I think this is the best way; that supports IE9+ and modern browsers.

function CustomError(message) {
    Object.defineProperty(this, 'name', {
        enumerable: false,
        writable: false,
        value: 'CustomError'
    });

    Object.defineProperty(this, 'message', {
        enumerable: false,
        writable: true,
        value: message
    });

    if (Error.hasOwnProperty('captureStackTrace')) { // V8
        Error.captureStackTrace(this, CustomError);
    } else {
        Object.defineProperty(this, 'stack', {
            enumerable: false,
            writable: false,
            value: (new Error(message)).stack
        });
    }
}

if (typeof Object.setPrototypeOf === 'function') {
    Object.setPrototypeOf(CustomError.prototype, Error.prototype);
} else {
    CustomError.prototype = Object.create(Error.prototype);
}

Also beware that __proto__ property is deprecated which is widely used in other answers.

Note: See discussion in the comments and @MattBrowne's gist.

In 2017, I think this is the best way; that supports IE9+ and modern browsers.

function CustomError(message) {
    Object.defineProperty(this, 'name', {
        enumerable: false,
        writable: false,
        value: 'CustomError'
    });

    Object.defineProperty(this, 'message', {
        enumerable: false,
        writable: true,
        value: message
    });

    if (Error.hasOwnProperty('captureStackTrace')) { // V8
        Error.captureStackTrace(this, CustomError);
    } else {
        Object.defineProperty(this, 'stack', {
            enumerable: false,
            writable: false,
            value: (new Error(message)).stack
        });
    }
}

if (typeof Object.setPrototypeOf === 'function') {
    Object.setPrototypeOf(CustomError.prototype, Error.prototype);
} else {
    CustomError.prototype = Object.create(Error.prototype, {
        constructor: { value: CustomError }
    });
}

Also beware that __proto__ property is deprecated which is widely used in other answers.

Note: See discussion in the comments and @MattBrowne's gist.

UPDATE: Added constructor assignment. See this test for comparison on different implementations. Test module here.

In 2016, I think this is the best way; that supports IE9+ and modern browsers.

function CustomError(message) {
    Object.defineProperty(this, 'name', {
        enumerable: false,
        writable: false,
        value: 'CustomError'
    });

    Object.defineProperty(this, 'message', {
        enumerable: false,
        writable: true,
        value: message
    });

    if (Error.hasOwnProperty('captureStackTrace')) { // V8
        Error.captureStackTrace(this, this.constructor);
    } else {
        Object.defineProperty(this, 'stack', {
            enumerable: false,
            writable: false,
            value: (new Error(message)).stack
        });
    }
}

if (typeof Object.setPrototypeOf === 'function') {
    Object.setPrototypeOf(CustomError.prototype, Error.prototype);
} else {
    CustomError.prototype = Object.create(Error.prototype);
}

Also beware that __proto__ property is deprecated which is widely used in other answers.

Note: See discussion in the comments and @MattBrowne's gist.

In 2016, I think this is the best way; that supports IE9+ and modern browsers.

function CustomError(message) {
    Object.defineProperty(this, 'name', {
        enumerable: false,
        writable: false,
        value: 'CustomError'
    });

    Object.defineProperty(this, 'message', {
        enumerable: false,
        writable: true,
        value: message
    });

    if (Error.hasOwnProperty('captureStackTrace')) { // V8
        Error.captureStackTrace(this, CustomError);
    } else {
        Object.defineProperty(this, 'stack', {
            enumerable: false,
            writable: false,
            value: (new Error(message)).stack
        });
    }
}

if (typeof Object.setPrototypeOf === 'function') {
    Object.setPrototypeOf(CustomError.prototype, Error.prototype);
} else {
    CustomError.prototype = Object.create(Error.prototype);
}

Also beware that __proto__ property is deprecated which is widely used in other answers.

Note: See discussion in the comments and @MattBrowne's gist.