Technically you can burn out the circuit with over charging. Maybe not too many devices but it's a general rule be wary of
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No you can't. As has been stated - the circuit in the One X battery controls the charging current, regardless of the charger's ability to supply a higher current.
If your charger can supply 2000mA, the One X will still only ever take 1000mA at most.
That said - if you buy chargers meant for the iPhone/iPad, they do not adhere to the USB charging spec, so the One X will only charge at a maximum of 400-450mA (in case it's plugged into a real USB port which is rated at 500mA max).
The difference between an "iPhone" charger and a "proper" one is this:
The D+ and D- lines should be shorted together on a "Proper" charger (like the one that comes with the One X or any HTC) - on an iPhone charger, the lines are not shorted. When the HTC phone sees this, it will limit its charging to 400mA.
This is why your phone will charge more slowly from a PC or non-compliant charger.
However, the screen and phone-on-state demands more than 400mA, so you will find that an HTC phone will actually drain when used for Sat-Nav in a car if you do not use an official HTC charger, or other compliant charger. Most generic ones are meant for iPhones and do not have the data lines shorted.
So, just so you are clear:
You cannot damage your One X by using a charger that is rated to a higher current - eg 2000mA.
The only way you might damage it is by using a charger that supplies more than 5V (lots more - there is over-voltage protection). But good luck finding a USB charger that does that.