The most common way to heat a house is with a furnace. And furnaces and air conditioners need their filters cleaned every couple of months. (How often you need to change them will depend on your filter and your furnace. You can see one person's cleaning ritual in this Energy Saver blog post from this spring.)
If your HVAC system is in dire straits, you may even want to clean out your HVAC ducts. This highly informative article from the EPA explains the entire process and explains when you may need to clean out your ducts and when you will not. They go to great pains to explain that just cleaning the dust out of your ducts will not necessarily increase the air quality in your home, though. And it certainly doesn't need to be part of your yearly home maintenance.
But no matter how you heat (or cool) your home, you want to make sure that the systems you're using have clean filters. This will ensure your appliances are working like they're supposed to. It could also help the air quality of your home, which will make life a little easier on those people among you who deal with allergies of any sort.