You can place your Mac mini on its side and use it if you like. Just be sure not to rest the computer on its front or back side or you'll block access to the slot-loading optical drive in front or port connectors in back.
Always place your Mac mini on a hard, flat surface to provide maximum airflow to the computer's vents around the rubber base. Don't put anything on top of your Mac mini or stack Mac minis on top of each other either. If your Mac mini is configured with AirPort or Bluetooth, you could hamper the signal strength since the antennas are located in the top of the computer.