The bore and chamber, as with most other firearms, are a given with the AR-15.

Though much of the military spends more time maintaining their weapons than they do actually training with them, a wise armorer once suggested I "follow the gas" when I looked at what REALLY needed to be cleaned.

After the gas tube, the first place the gases go in the AR is into the bolt carrier key. Pipe cleaners are about the only thing that'll work. The cas then expands inside the bolt carrier, causing the carrier to begin traveling rearward and the bolt to turn and unlock. I have to differ here. I've seen the guts of bolt carriers so gunked up that the firing pin couldn't make a reliable primer strike. Carbon will bake itself onto the innards of the bolt carrier and the tail of the bolt if you let it. I've never met a BCG that was "self-cleaning." Heaven knows how much I'd liked to have, though!

Another component that needs TLC from time to time, particularly when you're using junk ammo or when you're in wet or dusty environments is the extractor. That little cut that grabs the case rim gets gunked up, you're done.