Wow not a single response yet...
"Computers" encompasses almost EVERYTHING you can think of...
- hardware engineer
- software application developer (programmer/engineer)
- web designer/developer
- graphics / 3D design
- help-desk (software support)
- LAN administration
- networking
My personal stance on a computer career now... tough to get your feet wet without real world experience. Most jobs (depending on what you do) require 3-5 years professional experience before they even consider you a candidate. That's why you hear how a lot of IT folks are out of jobs... either that or they had to cut back a bit on the "extra" employees not critical to the business. 9/11 and the economy effects everyone... people stop spending, contracts don't get signed/renewed, less work for everyone. When you see the biggest of companies start to lay-off seasoned veterans, you know the industry is in trouble.
Starting a computer career now with the hope that you can earn a good living within the year probably won't be a good idea. If you have the resources in the meantime, by all means go with it since the economy can't stay this way for too much longer. Certifications and hands-on at home will get you started nicely. Message forums that discuss hardware/software problems are a good place to gain knowledge in many different areas... I started that way only 2 years ago... motivation is key.
Specific fields? There's ALWAYS going to be a need for programmers. Web developers who can code with dynamic languages are just as good. I think the Administration/Networking fields are too saturated, but they are pretty easy to "get into". Help desks are a good starting point if you are willing to do a contractor role... and to get your feet wet.
My 2 cents. Good luck.