Not every carbon in the molecule is asymmetric. movies was right in that chirality is usually referring to the whole molecule, however, my original question was concerning the chiral centers (also termed "stereogenic centers"). Not every carbon is a chiral center (or asymmetric carbon as you would put it) because many of them either have two or three hydrogens bonded to them (not pictured) or a double bond.
When you look at a molecule, look for sp3 hybridization. If there's four different substituents bonded to any carbon, the carbon is a chiral center. Make sure you take the molecule as a whole into account though. Like, if there is a phenyl group and a methyl group bonded to the carbon, it could be a chiral center because even though there are two carbons directly bonded to it, the larger structure coming off each bond is different.