Invoking a function without parentheses

There are several different ways to call a function without parentheses.

Let's assume you have this function defined:

function greet() {
    console.log('hello');
}

Then here follow some ways to call greet without parentheses:

1. As Constructor

With new you can invoke a function without parentheses:

new greet; // parentheses are optional in this construct.

From MDN on the new oprator:

Syntax

new constructor[([arguments])]

2. As toString or valueOf Implementation

toString and valueOf are special methods: they get called implicitly when a conversion is necessary:

var obj = {
    toString: function() {
         return 'hello';
    }
}

'' + obj; // concatenation forces cast to string and call to toString.

You could (ab)use this pattern to call greet without parentheses:

'' + { toString: greet };

Or with valueOf:

+{ valueOf: greet };

valueOf and toString are in fact called from the @@toPrimitive method (since ES6), and so you can also implement that method:

+{ [Symbol.toPrimitive]: greet }
"" + { [Symbol.toPrimitive]: greet }

2.b Overriding valueOf in Function Prototype

You could take the previous idea to override the valueOf method on the Function prototype:

Function.prototype.valueOf = function() {
    this.call(this);
    // Optional improvement: avoid `NaN` issues when used in expressions.
    return 0; 
};

Once you have done that, you can write:

+greet;

And although there are parentheses involved down the line, the actual triggering invocation has no parentheses. See more about this in the blog "Calling methods in JavaScript, without really calling them"

3. As Generator

You could define a generator function (with *), which returns an iterator. You can call it using the spread syntax or with the for...of syntax.

First we need a generator variant of the original greet function:

function* greet_gen() {
    console.log('hello');
}

And then we call it without parentheses by defining the @@iterator method:

[...{ [Symbol.iterator]: greet_gen }];

Normally generators would have a yield keyword somewhere, but it is not needed for the function to get called.

The last statement invokes the function, but that could also be done with destructuring:

[,] = { [Symbol.iterator]: greet_gen };

or a for ... of construct, but it has parentheses of its own:

for ({} of { [Symbol.iterator]: greet_gen });

Note that you can do the above with the original greet function as well, but it will trigger an exception in the process, after greet has been executed (tested on FF and Chrome). You could manage the exception with a try...catch block.

4. As Getter

@jehna1 has a full answer on this, so give him credit. Here is a way to call a function parentheses-less on the global scope, avoiding the deprecated __defineGetter__ method. It uses Object.defineProperty instead.

We need to create a variant of the original greet function for this:

Object.defineProperty(window, 'greet_get', { get: greet });

And then:

greet_get;

Replace window with whatever your global object is.

You could call the original greet function without leaving a trace on the global object like this:

Object.defineProperty({}, 'greet', { get: greet }).greet;

But one could argue we do have parentheses here (although they are not involved in the actual invocation).

5. As Tag Function

Since ES6 you can call a function passing it a template literal with this syntax:

greet``;

See "Tagged Template Literals".

6. As Proxy Handler

Since ES6, you can define a proxy:

var proxy = new Proxy({}, { get: greet } );

And then reading any property value will invoke greet:

proxy._; // even if property not defined, it still triggers greet

There are many variations of this. One more example:

var proxy = new Proxy({}, { has: greet } );

1 in proxy; // triggers greet

7. As instance checker

The instanceof operator executes the @@hasInstance method on the second operand, when defined:

1 instanceof { [Symbol.hasInstance]: greet } // triggers greet

The easiest way to do that is with the new operator:

function f() {
  alert('hello');
}

new f;

While that's unorthodox and unnatural, it works and is perfectly legal.

The new operator doesn't require parentheses if no parameters are used.

You can use getters and setters.

var h = {
  get ello () {
    alert("World");
  }
}

Run this script just with:

h.ello  // Fires up alert "world"

Edit:

We can even do arguments!

var h = {
  set ello (what) {
    alert("Hello " + what);
  }
}

h.ello = "world" // Fires up alert "Hello world"

Edit 2:

You can also define global functions that can be run without parenthesis:

window.__defineGetter__("hello", function() { alert("world"); });
hello;  // Fires up alert "world"

And with arguments:

window.__defineSetter__("hello", function(what) { alert("Hello " + what); });
hello = "world";  // Fires up alert "Hello world"

Disclaimer:

As @MonkeyZeus stated: Never ever shall you use this piece of code in production, no matter how good your intentions.