Connecting USB mouse to Galaxy SIII
Yes, you need an OTG cable. The pin layout is different than a regular micro USB to USB cable; essentially, it's equivalent to shorting pins 4 and 5 on a normal cable. This is what causes the phone to know that it needs to be the host rather than the slave.

In fact, you can do this yourself if you're handy with electronics and have a cable you don't mind taking apart, though they're also readily available at many online retailers (Amazon, Newegg, Monoprice, etc).