I am currently a sophomore at Rutgers New Brunswick and majoring in Computer Engineering. What should I be doing to increase my chances of getting a job after graduating besides good grades?
Learn relevant skills that employers need. The example for physics majors is to learn computer languages. For a computer engineer I assume that might not be the best example since I would assume you already know some. Talk to your professors and ask them what they know about what employers really what. Of course, as lisab said, internships would be great.
There are a lot of companies who visit Rutgers looking for people to intern, especially for computer science and engineering fields (so undoubtedly for computer engineering as well). So attending relevant internship fairs and company events on campus (for instance, Google is having a panel do a presentation in a couple weeks, PM me if you want me to send you the details) would be a good idea. Getting involved in some student organizations related to your field couldn't hurt either, because they often hold various talks related to jobs, not to mention that it is good to know the fellow people in your major, since most of them are in the same boat as you are.