Arduino Uno not appearing under ports
If the Arduino doesn't show up on multiple computers, and others do, it may be bricked, or dead. You might try reflashing the chip, and hope that solves your issue. If it doesn't, chances are it's toast.

If however the device simply doesn't show up on one computer, but does on another. It's either a software issue, or a USB issue with that computer.

If winblows OS, try reinstalling, or updating the drivers for the USB, as well as the Arduino. And check your power management on the USB as well. I've seen Windows USB poop the bed if a device is connected / disconnected, or restarted several times in rapid succession. When this happens, sometimes Windows will think the port or device is faulty, and simply stop responding to its presence.

If *nix, make sure you've configured it properly.