I already have a Schrader bicycle pump, which is pretty standard. But I didn't have a working Presta one so I decided to get a new one (that works) and in the event it ever breaks and I need an adapter, I therefore bought an adapter too. I call it the Mechanic's Rule of Tool Redundancy - when in doubt, get two or more in case you cannot find the other tool, it breaks, or cannot be used for whatever reason. This is why you can never have too many toolboxes, screwdrivers or tools in general.
Since the invention of the pneumatic tire many valve types have come along but for bicycles the two most popular that are still in use are Presta and Schrader (or as I like to call them, de French one and zee German one - not because that is their country of origin, just because they sound like they are French and German).
The Presta valve is the skinny one of the two and is slightly more cumbersome to use, having a lock nut instead of a spring to make sure it is closed and doesn`t leak air. The Presta valve is more popular on racing bicycles because it is skinnier and doesn`t leak air easily.
The Presta valve also enabled racers to inflate tires with a simple pump with attached chuck (pump head) and no hose. Having no valve spring to overcome it is therefore faster and easier to pump gas into the tires. If Schrader valves had a valve depressor it could speed up the process, but it would make the pump head larger, heavier and impractical.
Because of the small diameter of the Presta valve it requires a smaller hole in the rim, which means that the bicycle rims can be narrower. This saves on weight and increases overall speed.
However Presta valves break easier, are harder to fix, are not widely used except in racing bikes, and Presta pumps break easier too (based on my first hand experience with them). Some Presta valves have been made with removable cores to make them easier to fix, but demand is so small that they are uncommon. Removable Presta cores can be identified by two wrench flats on the coarse valve cap threads.
In contrast Schrader valves are robust, universally used, and have an easily removable core. And they are easier to fix. Spring closure makes them simpler to use because one needs only to press the inflation chuck onto them at any gas station that has an air pump. With foot or hand pumps, a screwed or lever chuck provides the valve depressor - and it can tell you what the pressure is in the tire too.
My advice for my fellow bicycle mechanics? Get a Schrader pump and a Presta adapter. You might never use the Presta adapter, but at least you will have it when you need it.