Can I use a charger with more output amperage than the device needs?

Yes, it is absolutely safe to charge a device with a charger that has more current capacity than needed.

Ohm's law tells us the relation between current, voltage, and resistance:

    I    =     V      /     R  
(current =  voltage  / resistance)

Since the voltage is held constant (5V), the only factor that determines current draw is the load (another term for resistance) the device places on the charger. Thus, the device will only draw as much current as it needs and no more.

Speaking from personal experience, I've had no problems charging my phone (which only draws 700 mA) with my Kindle charger (850 mA) or my iPad charger (2.1 A).

To choose the right charger for the right device increases the rate of charging, increases the lifespan of the device and decreases the risk of burn. There is always a risk of burn, but it can be minimized by many methods.

• Ohm's law V = R I where V voltage, R resistance, and I current. Choose a cable which has more/same charge capacity (I) than the phone.

General Summary

Exercises where try to answer the question marks

V (V) /   V (V) /
I (A)     I (A)
Cable     Phone     Decision
-------   --------- --------
5V 1A     5V 2A     No, burn risk
5V 2A     5V 2A     Yes 
5V 2.1A   5V 2A     Yes
5V 2.4A   5V 2A     Yes
5V 0.7A   5V 2.1A   No, burn risk  
5V 0.7A   5V 0.85A  No, burn risk

5.2V 2A   5V 2A     ?   
5.1V 2A   5V 2A     ?   
4.9V 2A   5V 2A     ?
4.8V 2A   5V 2A     ? 

5V 1A     3.8V 1.3A No 
5V 3A     3.8V 1.3A Yes
9V 3A     3.8V 1.3A ?
9V 3A     5V   2A   ?
5V 3A     5V   2.1A Yes (Edza case)

• burn risk - drawing more current from the cable which it supports is always a burn risk
  • feel the charger with your hand; if it is very hot, reject; overheating will happen; since most chargers do not have protections besides the covering, the seller cannot recommend combinations with burn risk

[new table here where device has Snapdragon 810 or 820, since the situation will be little different in dynamic configurations]

Practical table where try to answer the question marks

For most USB chargeable smartphones the battery voltage is irrelevant. The USB charging circuit is often set to 5 V 0.5 A

V (V) /          V (V) /
I (A)            I (A)
Cable            Phone      Decision
---------------  ---------  ----------
USB1 (5V, 0.5A)  5V 2A      ?
USB2 (5V, 0.5A)  5V 2A      ?
USB3 (0.9A)      5V 2A      ?
USB-C            5V 2A      ?
Apple's iPad
5V 2.1A          5V 2A      Yes
Amazon's 
Kindle fire 
5V 1.8A          5V 2A      No, burn risk
Car charger
5V 1A            5V 2A      No, burn risk 
Car charger
5V 2.1A          5V 2A      Yes

Sources

• Choosing power supply, how to get the voltage and current ratings?
• What would happen if I charged my phone with a 5V 1A or 5V 3A battery charger? The phone's rating is 3.8 V 1300mA.
• ...

Phones in examples: Oneplus 2, ...
Tools to study volt and ampere which your phone is charging: Ampere

Expanding on tapped-out's answer. These chargers work the same way the internal power of a desktop computer would work.

When you buy, for example, a gaming computer you will notice PSU (power supply unit) options exist which run way above and beyond the requirements of anything you could ever likely get inside the case. Obviously if the PSU controlled how much power was taken in by a component you would fry most systems fairly quickly. Clearly it is done by the components which require power.

It is useful to use higher PSUs when, for example, you might decide to upgrade your components at a later date. If your new pieces require more power than their counterparts they will simply take more in.

I don't think anything I run these days has the right power supply. My television runs from a laptop charger...