Which device utilizes a spinning mass to maintain orientation in multiple directions?

The gyroscope is the correct choice because it is specifically designed to maintain orientation and can measure or maintain rotational motion. This device uses the principles of angular momentum, where a spinning mass tends to resist changes to its axis of rotation. This characteristic allows it to provide valuable information on the orientation of the object it is mounted on, regardless of the direction in which that object is tilted or rotated.

In contrast, an accelerometer measures acceleration forces, which can determine changes in velocity and gravitational forces but does not inherently maintain orientation. A stabilizer is generally a system or device that helps to keep an object steady, often used in cameras or aircraft, but it is not a specific technology like a gyroscope. A magnetometer measures magnetic fields and is used for navigation or detecting magnetic materials but does not provide orientation with respect to rotational motion like a gyroscope does.

Therefore, the gyroscope's unique ability to maintain and provide orientation across multiple axes through its spinning mass makes it the correct answer.