Been keeping an eye on this thread, decided to chip in my 0.02 now.
There are a whole lot of engineering courses, but it's generally accepted that there's around 4 major ones.
Chemical Engineering is the application of physical and biological sciences to the process of converting raw materials or chemicals into more useful or valuable forms. E.g. a chemical engineer can be tasked with improving the process of converting raw materials into a useful form, or can be tasked with researching how to improve current materials.
Civil Engineering comprises the design, construction, and maintenance of the physical and natural built environments. As a civil engineer you can work on skyscrapers, airports, houses, bridges, etc.
Electrical Engineering comprises the study and application of electricity, electronics, and electromagnetism. As an electrical engineer you can work pretty much anywhere since technology (and electricity) is playing an increasing role in society. You can work for electricity companies, aircraft companies, tech companies, etc.
Mechanical Engineering comprises the design, analysis and usage of heat and mechanical power for the operation of machines and mechanical systems. Basically, if something has a moving part then chances are a mechanical engineer worked on it.
Universities of course offer more than these 4 courses, but they are all basically just some combination of these 4 (but go deeper in their field of study).
As AD posted,
this website is great for seeing which courses have the highest employment rates, but keep in mind that they just look at general full-time employment, not employment in that field of study. For example, a lot of aeronautical engineers who are employed full-time don't actually work in the aviation industry.
Regarding pay, graduate engineering salaries tend to be quite high (think around $60k). This of course varies depending on the company.
Another thing to keep in mind about doing an engineering degree is that it doesn't mean that you're only capable of doing engineering after you graduate. A number of people who study engineering end up becoming bankers or traders.