>Is it possible to get a PDA's serial number (running Windows Mobile OS) through .NET CF or some other API?
>

Yes. Here's an article from MS which will help:

http://msdn2.microsoft.com/en-us/library/aa446562.aspx

When I needed to do this I ended up just compiling this into a simple EXE which wrote the result into a known filename on the device. Then I used RAPI to run this EXE, then check for this file and read it out.

HTH