I've basically read multiple answers to this question. I've read:
Yes, 95% of original XBox games can play on the 360, if you have a hard drive (and a data transfer connector).
It can't be on the 4GB hard drive, it has to be at least the 20GB external hard drive or better.
It can't be any XBox360, it can only be the XBox360S with the 320GB hard drive.
You have to download an emulation program and than load that into the console as a disk.
You don't have to download an emulation program; you only have to login to XBox Live and the emulation program will later be updated into your system.
The hard drive has to be certified Microsoft XBox360 or the XBox games will not work.
I just went through a chat session with a support tech on here, and he thinks the used 20GB hard drive I have is not authentic Microsoft (even though it has Microsoft and XBox360 written and stamped all over it with labels that don't peel off). So you can judge that conclusion for yourself. He also said that when you go to Settings, then Memory, the 20GB hard drive should read "Microsoft" on the screen, otherwise it's not genuine. Mine didn't read that, it just read 6.1 GB (remaining).
Here's the deal. I've spent $50 on XBox games that can't be played on my 360 right now. I could buy a new 20GB hard drive for under $40 and try that one instead, or I could fork out $45 and simply get a used XBox and be done with all of this. However, it would be nice to keep everything on one console instead of two.
For the people on here with 20GB hard drives: does it say Microsoft on the screen in the settings for this hard drive, and if so, can you play original XBox games on a non-S 360? This will help my future decisions...thanks.