The two worst things that affect LiIon and LiPoly battery's are excessive heat and extreme low voltage. Sometimes they cant even recover from to low of a voltage. Its bad to let it go completely dead. The phone shuts off when the voltage/current get to low to protect the battery. If its not charged for a long time the battery will continue to self discharge and the protection circuit kicks in and the battery is completely non usable until voltage can be increased.
Phones and tablets have protective circuits built in and software to monitor the amount of voltage and current going into them.
Phones are designed to cut off around 1 Amp and tablets around 2 Amps.. Obviously every phone is different but these are the averages.
Years ago when we had flip phones, like the razr, those were 500 mAh. then the first smart phones were around 750 mAh. Now the standard is 1 Amp.
So when buying a home / car charger look to see what the output current is. If its 1.5amp then your fine, you wont utilize all of it. If you plug in a tablet then it will take all of it and want more.
The PROBLEM most people run into is cheap build quality. Unregulated DC power can fluctuate. The cig plug in your car is 12 volts, but the phone needs 5 volts. Theres a step down process. If the charger is made cheaply it doesnt regulate the voltage well when higher current draw is required and this can impact charging.
Why put a 2 dollar charger on a 500 dollar phone. Why risk it. Spend 10, 15, 20, 30 bucks on a good high quality charger that will work when its supposed to.