G. Mark’s Answer
There are many, many types of engineering. But the major branches that most folks are talking about when referencing these are Mechanical Engineering -- dealing with mechanical devices and more physical machines -- Electrical Engineering -- dealing with, of course, electrical devices and electronics. Then of course Chemical Engineering deals with chemistry and chemical processes. My post-graduate studies were in Computer Engineering, which is the subset of Electrical Engineering dealing with, of course, computers and digital electronics. As you can see, these area overlap quite a bit. For example, a Chemical Engineer would be unlikely to have not studied computers and some digital architecture. There's also Biochemical Engineering and Bioengineering, which focuses studies from the other branches on biological systems. There are other branches as well, but most of these are some amalgam of other branches. In general, you can't go wrong by studying outside your primary focus. One thing I've found is that having spent a lot of time taking courses in a wide variety of areas is that it's fascinating how often these other areas either come directly in handy or allow me to understand other facets of a problem. Something to consider is that it's estimated that roughly 70 percent of innovations come from apply principles from diverse fields other than the one the original problem occurs in. Seeing solutions from other points of view is one of the basic driving forces of what is called "Design Thinking", and it encourages the designer to look at the entire environment in which the client experiences the problem. It's also quite a bit of fun learning new stuff from folks. I'd encourage you to look at some articles on the web about this, particularly case studies in which these branches of engineering are applied.