There are few things left on the modern automobile that are as mechanically simple as a cable or hydraulically operated clutch. There have been three pedals on the floorboards of vehicles since the Model T. While the T didn't use a clutch as we know it today, its competitors of the same vintage, as well as the modern vehicles of today use the same clutch, brake, and accelerator order. The clutch allows for the smooth transition between gears. Without the clutch, one must match revs when shifting and even then the gears will occasionally crash into one another when changing from one to another.
Learning to drive for many people over the age 60 today involved learning the delicate foot dance between the clutch, brake and accelerator pedals. Many of these individuals chose to drive automatics later, but they learned on manuals and can drive them today. I bring up this point because being able to drive a manual transmission can come in handy even in todays world. The skill of being able to drive a stick shift can be useful when renting a car outside the US, taking the keys from someone with both a stick shift car and a high blood alcohol content, and buying the only manual car on the dealership lot that they, the dealer will sometimes deal more on just to get rid of it.
The advantages of well driven stick shift over automatic include less maintenance, higher city fuel economy (most of the time), more power, more control, and finally theft protection. I state his last advantage because one has to be able to drive manual in order to steal a manual car.
The trends over the last 15 years have put the mechanical manual transmission on death row. There are many cars today that include two gates on their automatics like the Tiptronic system that Audi/VW/Porsche use. These systems allow drivers to manually shift through the gears of an automatic. Some even go further and use real manual gear boxes like VW's Twin Clutch system and BMW's Sequential Manual Gearbox (SMG). In these systems computers push in the clutch and match RPM's automatically while the driver can opt to either shift gears themselves or let the computer complete the shift.
While the automatic/automated manual gear boxes will probably replace most stick shifts in the coming years, there are those that cling to the third pedal and won't drive anything else. For the US market only, BMW most recently had to reverse engineer a stick shift gear box to work with their current M5, a car that was never designed to work with anything but SMG. I suspect though with time manual transmissions will go to the same place as carburators, manual chokes, crank starters, speedometer cables, and tube tires. Due to advances in technology, the third pedal will probably become more of a novelty than a genuine option on cars in the future.