Computer engineering, computer science, electrical engineering, chemical engineering, and materials engineering aren't going to go away any time soon because those continue to be burgeoning industries. Until something replaces electronics and computers and chemical processes and materials, we will need engineers to work on those. Many people will say that civil engineering isn't a hot career anymore. Same with aerospace. Both of those areas depend a lot on politics, as the main customer is often the government. If the politicians decide they want to build more bridges and war planes, those areas look hot. If they scale back, not so much. Best to look at what the salaries are like for those careers.
Some people predict a decline in the demand for mechanical engineers due to a decline in the American auto industry. I don't really know. I mean, mechanical engineers do a lot more than just cars. Like I said, anything with moving parts is a mechanical engineer's domain.
Be forewarned that the hotter the engineering career, the more math-intensive it is. Even computer science is very heavy on math, just a different kind of math (called discrete math) from calculus or vector analysis.