There are a few of possibilities I can think of.
The USB cable could have gone bad. Try a known-good cable.
The driver in the computer could have become corrupt. Delete the phone (in Device Manager, if you're running Windows), plug the phone in and when it asks to install the driver, tell it you have the disk. Then find and select the driver you downloaded. (If you don't know where it is, download a new copy from the Samsung site.)
The USB port in the phone could have gone bad. The best test for that is a friend who has a Samsung phone that connects to his computer. See if yours connects to his computer using his cable. If not I'd suspect the USB port on your phone. (Fixing that is usually done by replacing the motherboard. Very few people want to get involved in replacing the port itself.)