Different devices pull at different rates. They're often limited more by how quickly they can charge the battery without damaging the battery. There are some devices (no smartphones that I'm aware of) that run off capacitors instead of batteries, with one of the upsides being VERY rapid charging (and a downside of not being able to hold a charge as long). So, as already said, buying a higher amperage charger than your device was made for doesn't increase the charging speed. It does, however, future-proof your charger, in that if your next device is made to pull more juice, you won't be stuck with a charger that can't keep up. Also, many of the aftermarket chargers have more than one USB port on them, and the higher amperage allows it to keep up with charging two devices, as generally the amperage is the total output of the charger. So if you have a 2.1a charger with two ports, and you plug in two devices that each want to charge at 1.5a, then they're not going to be able to charge at full speed, as that would require 3a. However, if you were to plug in two devices that each charge at 1a, then they should both charge at full speed.
Note that there are also some different charging standards. Some of my aftermarket chargers are marked with "A" and "N/A" beside the two USB ports. One is set up Apple-style, the other to the other standard. Some devices seem to be happy to charge from either, while others are finicky. Generally, if I plug into the port it's finicky about, it'll still charge, but very slowly.
My hope is that companies will switch to the USB 3.0 like Samsung did for the Note 3. It charges significantly faster, it's what I miss about my note 3.
There is a consortium that decides the standard plug style for charging mobile devices. Participation is voluntary (though I believe there are some countries that are now requiring use of the standard, though I think Apple has managed to get around this with adapters or something so far), but most major manufacturers have decided to participate. The current standard is Micro USB. I believe I've read that they've already decided that the next standard will be USB 3.1 Type C, but they are still finalizing the design. It will be smaller than the USB 3 on the Note 3, and reversible.
Upcoming Reversible USB Cable Depicted in New Renderings - Mac Rumors
*Edit*
Found more info on the charging standards.
http://en.wikipedia.org/wiki/Common_external_power_supply