As multi-core processors become more and more popular, I think it would be wise for me to become familiar with how to write code to take advantage of them. I am a .NET developer, and am not sure where to begin (seriously, I have no clue where to start). Any suggestions?
Multi-core programming is essentially multi-threaded programming. As long as your application is multi-threaded, the operating system will determine which core to run which thread on.
So then, your real question should be, what kind of applications would benefit from being multi-threaded? Think of such an application, then instantiate multiple threads to solve equal portions of the problem.