As noted above, there are some things you can do to help cut dust down from getting into the pc. IE filters.
However, this is only combating the symptom and not dealing with the bigger issue and that is eliminating the dust source.
The problem is we all emit dust, carpet as noted above does not help the matter, pets, smoking all add to the problem.
If you don't have any pets, don't smoke, removed the carpeting those are all big steps to cutting the problem out.
The next step above all these that may help much more relates to the HVAC system in the house. If the computer room is situated in a bedroom that is closed off from the rest of the house and the door is closed alot consider putting in a return grill with a filter. Normally computer rooms in a home are small and most likely a 12x12 return grill is adequate.
These filter sizes are generally hard to find unless you shop for them over the net and buy them a dozen at a time.
The reason why this is important is if the room you are in is closed up most of the time there is a natural draw from the room even though the door is closed. Air is being pushed into the room.
If your HVAC system return is undersized... which by most standards this is the case 99% of the time; even if the house is new, this is very much often the case.
When the HVAC system first comes on if the door of the room is closed the room goes under a negative pressure, which more or less means air is sucked in anywhere that there are cracks and crevices, this is either at the base of the door, windows etc.
Because there is no filtered return in the room dust will accumulate in the room because it has no way to get out, by adding a return to the room, you equalize the pressure and thus don't suck in more dust and what dust you do have is sucked into the filter of the HVAC system.
Additionally once this return is installed you could run the HVAC system with fan on to keep the air circulated and keep dust accumulation to a minimum.
This won't cut dust out entirely but it will greatly reduce the dust bunnies to an absolute minimum.
Additionally duct work leaks can cause the same things or worse to occur, and depending on the age of your system this could drive the implementation cost up quite a bit if you need more than just a new return... as it makes little sense to add one thing when the entire duct system is shot.