First off, don't listen to these kinds of people (>>2352).
I work for a downstream refining company. I specialize in separating polymer precursors from the nasty-ass bottoms off the main distillation columns. I'm 24, and I make over $120k a year. Look anywhere you want and you will find the same thing: Petros are paid more than any other subset of engineering. See: http://www.bls.gov/ooh/architecture-and-engineering/ for good data on all engineering occupations.
Outlook: it is highly dependent on the price of oil. When oil dropped sub-$50, people were being laid off left and right on the extraction side, while there were only minor layoffs on the refining side. You will still be making a lot of money either way. Interestingly, midstream is the most boom and bust of the three sectors of the oil and gas industry. The key is to be either A) really damn good at your shit or B) get into management.
Respect: Depends on who you talk to. An environmentalist will always bear hatred for you, while your bank account will love you. My mom works for a biofuels company and she has some resentment, but is glad that I can support myself. If you work on the downstream side many of the processes there (separations, heat transfer, fluids) translate into other Chemical Engineering related fields, like chemical manufacturing, food processing, and biofuels.
Now for my next point: a petroleum engineering degree is not the best degree to get. Early in your career it can be a slight hindrance unless you specifically want to do oil. After about 5 years, it's more about prior experience than your degree. It also pigeonholes some of the concepts that work in other fields to oil and natural gas. It's worth having exposure in reactor kinetics and biological processes in addition to the transport side that a PetroE degree would heavily emphasize. Remember that chemical engineering is both a very broad and very specific field that is composed of these subfields (including ChemE itself):
-Petroleum Engineering
-Chemical and Biological Engineering
—Biomedical Engineering
—Biological Engineering
—Genetic Engineering
-Materials Science
-Mining Engineering
-Environmental Engineering
-Nuclear Engineering
-Agricultural Engineering
-Pharmaceutical Engineering
Chemical and related fields are so broad and diverse, so my recommendation is that you get a ChemE degree. If you're into energy, you can do renewables, bio-derived, or sweet, sweet crude. If you like materials, you can do polymers, ceramics, and even electric components like >>2354 suggested. If you like chemicals there is everything from pesticides to organic cleaners. ChemEs do semiconductors, WD-40, and even the dyes in your clothes. We're everywhere.
Trust me, you have no idea what you're really into when you're 19. Don't pidegonhole yourself just yet. I'm saving up money so I can go to law school and do patent law. I love petro, but I worked on a project that involved some patent law and processes concerning a new method of separation for some of the nasty crude. I had taken a class on it in college and was immediately assigned to lead the patent research with the legal team. I fell in love with it (again) and decided to start saving for law school. Pick something that is broad enough to give you options, but specific enough to be relevant to your interests.
I'll tell you what I tell every college freshman that I mentor when they hem and haw about which major to choose: whenever someone invents something or makes a variation on a current product, it will have to be made in bulk. Whenever you make something in bulk, you need a lot of chemicals. These chemicals need to do things in a very specific manner to make the things that will build what was invented or designed. That's where we come in.