This seems to be quite a common problem, and there are a number of problems, each with their own solution.
- Make sure you have selected the right Arduino board in your IDE
- Make sure you have selected the right serial port in your IDE (when you unplug your board, it should disappear).
- Make sure you do not have anything plugged in to the tx & rx pins (usually 0 and 1).
- Make sure your Atmega chip has a bootloader on it
- Try another cable
- There may be a problem with your computer - try another computer
- If using another helps, try reinstalling the USB serial driver
- Try unplugging the Arduino board, holding down the reset switch, then plugging it in (still holding down reset); continue to hold down reset for about 5 seconds.
- make sure nothing else is trying to use your serial port