it's happened to me quite a bit
but it could be two things:
1) your USB port is in fact busted
2) your computer just doesn't recognize the device
two things to narrow it down
is your phone able to be charged (ie the red light comes on when the charger is plugged in)?==
yes?=your USB port works fine, your computer doesn't have the correct Drivers
no?=your USB port is screwed

(reason=if it charges, the port [charge portion] obviously works fine--it's just any peripheral device like a computer that's not recognizing it b/c it has insufficient software/Drivers to recognize it as a Mass Storage/Disk drive)
try this--it works for me all the time
turn off the phone, take off the battery, remove the SD, re-insert the SD card, put in the battery, turn on the phone. then try connecting it to the computer once it's fully booted.
also, check your Computer-Settings:
Menu>Settings>Connect to PC>Default Connection Type>select Disk Drive
quite often, mine gets switched back to "Charge only" for some reason and i have to manually change it repeatedly.
this is a really common problem, so give this a shot before writing it off as a broken USB port