I agree with the "accepted" answer, but it doesn't exactly reply to the question in mention: "should I go bigger than 1024px?".
Let's say we cannot afford to do a responsive/fluid design on every page. Let's be honest, not even Microsoft could afford this. Apparently, as soon as you leave their home page, it goes back to a 960px. It is understandable. As web designers, we sometimes are forced to get the job done as soon as possible.
So, should we go bigger than 1024px? I think it is about time we do.
For the past 4 years, my company has been creating 960px websites and ecommerces in order to fit this paradigm of the minimum resolution. However, times have changed. I believe 1024px wide resolutions are almost dead.
I was doing a little bit of research by reading the analytics of a ecommerce site that receives a decent amount of traffic (500,000 visits), from everywhere in the world, and only less than 5% of desktop users had a resolution of 1024px or less. And I would imagine the likelihood of these users converting is closely related to the amount of money that they would spend on a monitor.
Since a few months ago, my team and I decided to upgrade, and leave behind the myth. Now for us, a reasonable minimum resolution is 1280x768. Our designs now have either 1060px or 1180px width and they give us much more room and flexibility to be more creative. More room gives more breath to the message that we try to communicate, and somehow also to the user to have a better experience.
I know what you must be thinking: ..and what about the iPad? OK, iPad support is important in life and in general. A quick solution for us is the following markup that will make your website fit to the iPad screen resolution. It is pretty awesome!
<meta name="viewport" content="width=1180">
This is all based solely on my opinion. I would actually like to know what other people think.