Class methods as event handlers in JavaScript?

ClickCounter = function(buttonId) {
    this._clickCount = 0;
    var that = this;
    document.getElementById(buttonId).onclick = function(){ that.buttonClicked() };
}

ClickCounter.prototype = {
    buttonClicked: function() {
        this._clickCount++;
        alert('the button was clicked ' + this._clickCount + ' times');
    }
}

EDIT almost 10 years later, with ES6, arrow functions and class properties

class ClickCounter  {
   count = 0;
   constructor( buttonId ){
      document.getElementById(buttonId)
          .addEventListener( "click", this.buttonClicked );
  }
   buttonClicked = e => {
     this.count += 1;
     console.log(`clicked ${this.count} times`);
   }
}

https://codepen.io/anon/pen/zaYvqq