unable to connect samsung galaxy s3 via usb cable
So there are several things that could be happening.


Bad cable: it happens, not too often but often enough. Try a different cable if you can.
Improper drivers: you don't have the necessary drivers installed on your computer. Look here: http://www.samsung.com/us/support/downloads
Phone is in the wrong mode. When the phone is connected, there may be a notification telling you that it is connected, touch the notification and change the mode from MTP to PTP (or visa verca).


If those aren't it leave a comment with a few more details and I can try to help you out