There are some cases with dust filters like the Cooler Master Storm Stryker/Trooper (Has filters on the bottom, on the 5.25 inch drive bays, and on the top), or the Antec P280.
The Fractal Design R4 also has dust filters and sound deadening material in the top and side vents.
Also if you have a positive air pressure in your case (With more intake fans than exhausts fans) the dust is going to be more difficult to get into your case.
But as chestercorgi said, you'll have to clean the case periodically.
My current build uses an Antec 900 but ever sinc I moved to Arizona, the amount of dust that accumilates over time has skyrocketed. I am aware of my need to dust the PC out periodically but I am looking for a case that wouldn't be as high mantenance as my current built.