I cannot figure out the difference between Mathematica and Mathematica Home Edition. Is it the case that Home Edition is less powerful or is it the case that Home Edition has limited use (noncommercial, etc.)? If it is less powerful, what doesn't it have?
General
Q: Is Mathematica Home Edition for anyone using Mathematica at home?
Yes. For years, people have been excited about using Mathematica to "play" or to pursue serious research outside of their commercial or academic jobs. Now Mathematica Home Edition provides an inexpensive version of Mathematica for those who want to use its powerful technology to explore their ideas. For those who want to integrate Mathematica into their teaching, research, or work, Mathematica Professional is always available.
Technology and Capabilities
Q: How is Mathematica Home Edition different from the professional version of Mathematica?
Mathematica Home Edition is a fully functional version of Mathematica Professional with the same features.

Bitten by the licensing bug again! Though it's nice for them to offer it. – Phoshi Oct 1 '09 at 20:53

1From the product summary: "Mathematica Home Edition is a 32bit program available for Windows (XP/Vista/7), Mac OS X (Intel), and Linux." So you don't get the benefits of the 64bit programs offered with the other licenses. Not much of a limitation for home users. – Brian Jan 25 '12 at 22:16

My Home Edition is 64bit (Linux). I think Wolfram allows you the option of 32 or 64bit now. I held off purchasing a Home license for more than 3 years until they made the 64bit version available. I don't need 64bit.... it was just the principal of keeping my system 100% 64bit.
I think the Home Edition limits the number of kernels you can run. My system information states "Max License Processes" "2".
I found a comparison of the different editions here: http://www.wolfram.com/mathematica/howtobuy/industryindividuals.html . According to that, there are only few limitations, namely a lower number of parallel computing kernels and less WolframAlpha API calls per day.