Update 2020:

With addEventListener() and querySelector() being supported in all major browsers, it can just be

document

  .querySelector('#the-important-button')

  .addEventListener('click', ev => ev.target.style.display = 'none');

<button id=the-important-button>Click</button>

Answer in 2012:

To make it unobtrusive and work on earlier IE and other modern browsers:

the HTML:

<button id=the-important-button>Submit</button>​

JavaScript:

var theButton = document.getElementById('the-important-button');



function hideTheButton() {

    this.style.display = 'none';

}



function addEvent(target, type, handler) {

    if (target.addEventListener) {

        target.addEventListener(type, handler, false);

    } else if (target.attachEvent) {

        target.attachEvent('on' + type, function() {

            return handler.call(target, window.event);

        });

    } else {

        target['on' + type] = handler;

    }

}



addEvent(theButton, 'click', hideTheButton);

Note that addEvent is a generic function that works well on earlier IE and other modern browsers. You can add other events similar to the last line of code above.

Sample on http://jsfiddle.net/W37Fb/5/