The three major options are Accelerometer, Rate Gyroscope, or Magnetic Compass. All three are available in chip form.
Accelerometer: Detects changes in speed. When speed isn't changing detects orientation relative to gravity.
Rate Gyroscope: Detects rate of rotation.
Magnetic Compass: Detects orientation relative to local magnetic field.
Many people use a Wii controller Nunchuck which includes an accelerometer and several controls. It is easy to connect to the Arduino.