Here are a few examples of the different types of brakes that Deb described.
(Sorry, crummy photos, but hopefully they'll get the point across.)

These are cantilever brakes, on Lee's Atlantis:



These are centerpull brakes, on Lee's Saluki, which used to be my Saluki:



These are "regular reach" sidepull brakes, on my Riv, Dusty:



And these are "long reach" sidepull brakes, on my Romulus, Pokey. Pokey used to have regular reach sidepull brakes, but then I switched from 700c wheels to the slightly smaller-diameter 650B wheels (for better clearance for larger tires + fenders), so the long-reach sidepull brakes accomodate the longer distance between the wheel rims and the brake mounts.