I Have tried everything i can find to connect my galaxy S3 to my computer, I have used different cables, and Different ports on my computer. My phone will connect to other computers just fine, but on mine it says "Can not recognise USB device. please reconnect and try again." Is this a computer issue, or just my phone?
Samsung has a webpage here for drivers for development purposes (ADB things) but I believe they will work for transferring files as well.
I had a very similar problem some time ago with my S3. The phone would connect and try to install drivers, but at the end the phone still wouldn't show up no matter how I tried to connect it.
If I recall correctly, I had to use the drivers that were shown on this XDA thread. Hope it helps.