Wow. There are so many possibilities.
By "computer engineer," I assume you mean someone with hardware and software skills both - you can set up a scope, run a debugger, and use information from both of them at the same time. You can fix the system with a soldering iron, text editor and compiler, or both.
Product development is one area. There are computers in everything these days (50 to 100 in any new car, probably a dozen just in your kitchen), and they all need to be wired to sensors and actuators, built into circuits, and programmed.
System development is another, integrating all kinds of boards into a backplane, writing the drivers for them, and making the whole thing work.
Chip manufacturers (nVidia, Intel, Altera, Freescale, ...), need people to specify, design, test, and apply the new chips. They also need people to write compilers, linkers, and debuggers, and to advise the chip designers about how to make the chips more software-friendly. Field and apps engineers need computer engineering skills to help customers put the chips to use.
Specialized areas include signal processing (video, audio, media, radar, medical instruments), medical imaging (CAT, MRI, etc), scientific (mass spec, gas chrom, PCR) and lab instruments (scopes, emulators), and too many others to count.
Then there are teaching, writing technical manuals, patent law, technical marketing and sales support, and other non-technical jobs that need technical backgrounds.
Then there are the hundred of others I haven't mentioned.
(I completed my PhD in computer systems engineering last year.)
Answered By: Tom V - 10/26/2007