if checkbox is checked, do this

It may happen that "this.checked" is always "on". Therefore, I recommend:

$('#checkbox').change(function() {
  if ($(this).is(':checked')) {
    console.log('Checked');
  } else {
    console.log('Unchecked');
  }
});

Try this.

$('#checkbox').click(function(){
    if (this.checked) {
        $('p').css('color', '#0099ff')
    }
}) 

Sometimes we overkill jquery. Many things can be achieved using jquery with plain javascript.

I would use .change() and this.checked:

$('#checkbox').change(function(){
    var c = this.checked ? '#f00' : '#09f';
    $('p').css('color', c);
});

--

On using this.checked
Andy E has done a great write-up on how we tend to overuse jQuery: Utilizing the awesome power of jQuery to access properties of an element. The article specifically treats the use of .attr("id") but in the case that #checkbox is an <input type="checkbox" /> element the issue is the same for $(...).attr('checked') (or even $(...).is(':checked')) vs. this.checked.