List of Engineering degrees you can find online and their relevance to Mechanical Engg -
Acoustic Engineering - Somewhat related;
Aerospace Engineering - Relevant;
Agricultural Engineering- Somewhat related;
Applied Engineering- Relevant;
Architectural Engineering- Relevant;
Audio Engineering- Somewhat related;
Automotive Engineering- Relevant;
Biomedical Engineering- Relevant;
Chemical Engineering- Somewhat related;
Civil Engineering- Relevant;
Computer Engineering- Relevant (Builds logic required for programming);
Electrical Engineering - Unrelated;
Environmental Engineering- Relevant;
Industrial Engineering- Relevant;
Marine Engineering- Relevant;
Materials Science Engineering- Relevant;
Mechanical Engineering- Relevant;
Mechatronic Engineering- Relevant;
Mining and Geological Engineering- Somewhat related;
Molecular Engineering- -Unrelated;
Nuclear Engineering- Relevant;
Petroleum Engineering- Somewhat related;
Software Engineering- Relevant (Logic development);
Structural Engineering- Relevant;
Telecommunications Engineering -Unrelated;
Thermal Engineering- Relevant;
Transport Engineering- Relevant;
Vehicle Engineering- Relevant;
So from list above you see that Mechanical Engg. is relevant to many (if not all) fields.
A mechanical engineer is a type of engineer. The list of all the different types of engineers is very long and varied. Every product you see around you was designed by at least one type of engineer. Mechanical engineers design physical things that move or have shape. Examples range from jet engines, with lots of intricate moving parts, to something as simple as a chair that has to be strong enough to hold a person, but slightly flexible so the chair is comfortable. Mechanical engineers learn how to analyze the strength of physical parts and the ways that parts fit together and move. Mechanical engineering appeals to people who like to design things that they can see and hold in their hands.
To add to the responses above, based on my experiences with my Mechanical Engineering colleagues, I have found that Mechanical Engineering is one of the more broad types of Engineering majors to study in college. By that I mean that the fundamental skills all Mechanical Engineering students learn are applicable to a wide variety of industries (e.g. Renewable Energy Company, Automotive Company, Medical Device Company, or even a consulting firm). Furthermore, there are a substantial number of concentrations you choose as a Mechanical Engineering student, like Aerospace, Energy Systems, Mechanics, Robotics, or other areas.
I would recommend looking at the courses/concentrations listed on a few College/University websites under Mechanical Engineering to learn more about what the course entails and what specializations are available to you.