USB 2.0 Host PC enumeration requirement
This will depend on if and how your device uses data.

The very old standard was 100mA by default, however in my personal experience, data ports made since 2010 will likely deliver 500mA if a data connection is detected, and more than 500mA if there is no data. 

This can be observed by plugging a phone into a computer and measuring the current. A standard USB cable will pass-through all 4 pins, and the data connection will be detected, resulting in 500mA current. 

BUT, reconfiguring the data pins can allow for more current. Observe three configurations below: 



Charging at higher current whilst also using data can thus depend on the configuration of host and client, and also the cable in between.

See this page for in-depth details:
https://www.maximintegrated.com/en/app-notes/index.mvp/id/5801

"Dumb" devices with no data (such as a USB fan) either don't have a connection to the data pins, or have them tied together in some way. 

Some ports, again those in computers, will detect overcurrent and be automatically disabled. Cheap wall chargers will not have this function, and may instead allow the voltage to drop, and may eventually burn out, sometimes in a dangerous fashion.