I always charge my iPhone with the charger that comes with it but I was wondering could I use different kind of USB devices to charge my phone? Will it damage my phone?
You can charge an iPhone with any reputable USB charger, but unless it is designed for Apple will charge very slowly (~100mA the USB default).
In some cases (this is based on earlier iPod dock) the device will refuse to charge if it incapable of negotiating a charge rate.
You would have more luck plugging into a computer. This will still be slow, but should be capable of negotiating a 500mA rate).