Confusion about current and voltage
Think as power supplys as a constant voltage, rather than the current they can provide. So a constant voltage supply will try to maintain the same voltage independent of the load you put on it (until, as you said, it blows up). So, a fan is designed to "pull" or "let pass" 1A for a given voltage while an air conditioning device is designed to "pull" 10A for the same given voltage. Thats why they pull different currents. And, while you can "force" more current with more voltage, some devices are smart enough that they will try to compensate for that using their regulators (switching or linear) by having their own constant voltage supplies on the inside, thus maintining about the same current consumption up to a given voltage. Normaly supplys fail not because they fail to push the current, but because they fail to provide the current that is being "pulled". If you have a constant current supply, when you try to "push" more current to a given resistive load, the voltage will rise.

About the phone, battery charging ICs will often have a limit to the current they can charge (as will the batteries). Often on cellphones that limit is close to 1A. Hence you can charge it faster on 1500mA. The 200mA rating is probably based on the USB standard max current, and is obviously easier for the manufacturer to supply you with the phone because its cheaper than a 1500mA supply. 

p.s.: to better understand different current draws for same voltages: http://en.wikipedia.org/wiki/Ohm%27s_law also remember that not all loads are resistive(most arent)