What is the engineering field in the largest demand today?

Computer Systems Engineering and Civil Engineers are two fields with a high demand for graduating engineers.

Pete Sturtevant, P.E.

The answer to that question depends on where you want to live, how much you want to make, and most important...what excites you. Engineering takes a lot of creativity, and that creativity take passion for your work. There are many thousands of engineering jobs across many disciplines at any one time. Here are some ways to think about it....
Do you want to live in the mid-west? There are many engineering positions related to automotive and heavy manufacturing. Mechanical engineers and Electrical Engineers are typically in high demand
Like sunny California or another tech hub like Austin, Boston, etc? Be a software, computer, or electrical engineer and specialize in devices and integrated chips
Like the gulf coast or want to explore the world? Petroleum engineers have great careers...when oil prices are booming and refineries are producing. They often have some of the highest pay too.
More into the North East? Pharma may be your path, and Industrial engineering or chemical engineering may put you into your career path.
People build roads and buildings nearly everywhere, and big cities have some of the toughest Civil engineering challenges.
Want to go green? Environmental Engineering is a rapidly growing field and often tied to government contracts. You should think about being near capitals.
Obviously most industries are semi-diversified across the country, but you get the idea. Engineers in general are always in demand and get more job offers than nearly any other field when graduating college. The college you graduate from, your grades, and your internships open the door to how many offers you're likely to get in the field you want when you graduate. That's just 4 years into your career though. You have another 40 or so years that you need to work, and that work needs to be exciting for you if you are going to succeed. Plan for the 40 years, and think about the industries most likely to be thriving in the 5-10-20 year horizon.