Instead of a cable in a housing, one can use a tube of liquid in a hydraulic system:

For the rear brake, it is possible to have rear pressure on the pedals act as a brake. This can either be direct, as in a fixed gear bike, or via a drum and freewheels as in a normal coaster brake:

Then you have the most common internationally, the rod brake. This is used primarily on roadsters and is a very reparable design. It's lever actuated and then either directly pulls up on the pad (front) or pulls through a series of linkages first (rear):

An alternative to the standard rod brake is the style used on swiss army bikes where the rod pushes the brake pad down on the top of the tire instead of up on the rim. It needs a different lever design than the normal rod brake beacuse it's moving the rod in the opposite direction:

Finally, there may only be one bike like this, but Sheldon Brown had a road bike set up with a toe strap taking the role of a cable on a caliper brake: