[Verizon Samsung Galaxy S 4] Marine6680:
A little knowledge of how Li-ion batteries charge is an important thing. Li-ion batteries have special charging requirements.

The part you plug into the wall... thats not a charger... its a power supply. It provides a 5v DC output at up to 2 amps.

The charger is built into the phone, and it determines how to use that available power to charge and power the device.

Li-ion batteries charge in a two stage cycle that is called "constant current/constant voltage". It is also important to know that a battery's voltage drops as it is discharged. (this voltage drop is how the battery meter gets its information, as it is predictable when tested under constant loads... the variable load of a phone is why the meter seems to be inaccurate at times)

During the first phase, "constant current", the battery is fed a constant current at the same voltage as the battery is currently outputting. As the battery takes in energy, the voltage rises but the current is kept constant.

The second phase, "constant voltage" starts when the battery reaches its highest voltage. (or more accurately, its highest safe voltage, which is around 90% capacity) During this second phase, the battery is fed a constant voltage, (the max voltage) and the current varies. The battery will draw as much current as it is able, and this rate slows naturally as the battery reaches full capacity. When the current drops lower than a certain set amount, the charger stops the charging process and the battery is said to be fully charged. This second phase is slow compared to the first phase, and that is why it can seem like the last 10% of charge takes longer than any prior 10%.

Some phones use the power supply to both power the device and charge the battery, the battery is electrically isolated during charging... but most charge the battery without isolation. Either way, the power from the power supply is being used to both charge and power the device, and this limits the charging speed.

This also limits the maximum capacity the battery can be charged to while in the device, because the voltage/current measuring is less precise. Unfortunately for these phones, the charging is controlled by software, and not simple hardware circuits that are isolated from the battery power. In fact, even when charging the phone with the power off... the phone is still actually powered up but in a low power background mode. This mode is actually a special screen off recovery mode. CWM recovery has had several instances of bugs, where the phone could not charge if the battery died to the point of powering of the device. Because the phone could never power into the special mode to start charging, due to this special mode being missing from, or bugged in CWM.

Also... these batteries have on average a 2-3 year lifespan, and also limited number of recharge cycles. The 2-3 year life is the same even if the battery is unused. As the battery ages, it looses capacity.

Charging at slower rates is better for battery lifespan than higher rates. Now the batteries in the S4 and especially the Note 2 are larger, and 2A is still considered a fairly slow rate, but of course 1A is even better. If you tend to charge only at night while sleeping, it may be better to use a 1A charger.