Can I construct a JavaScript object without using the new keyword?

What's wrong with using the new keyword?

At any rate, it sounds like the best thing to do is read up on Javascript inheritance: http://javascript.crockford.com/inheritance.html

You can use this pattern:

function SomeConstructor(){
   if (!(this instanceof SomeConstructor)){
        return new SomeConstructor();
   }
   //the constructor properties and methods here
}

after which you can do:

var myObj = SomeConstructor();

In addition to this (rather old) answer: you can use a module pattern to create an object:

function Person(name, age, male) {
  name = name || 'unknown';
  age = age || 0;
  function get() {
    return ['This person is called ', name,
            (!male ? ', her' : ', his'),' age is ',
            age].join('');
  }
  function setAge(nwage) {
     age = nwage;
  }
  return Object.freeze({get: get, setAge: setAge});
}
// usage
var jane =  Person('Jane', 23)
   ,charles = Person('Charles', 32, 1)
   ,mary = Person('Mary', 16);

console.log(jane.get()); //=> This person is called Jane, her age is 23
mary.setAge(17);
console.log(mary.get()); //=> This person is called Mary, her age is 17

Here's a jsFiddle for some Date functionallity I created using that pattern.