Question: My old cell phone number had made lots of calls I am not familiar with. I was confronted with a list of calls I know I did not call. I was also told that I was using Skype. I have never used skype, I do not know how to work that program. But, the cell phone company submitted a history of calls made. I called several of these numbers and I do not know the party on the other line. I even asked them if they have ever spoke with me or even recognized my voice, and they said they didn't know me or recognized my voice.
So my question is, is it possible that the cell phone company or someone close to me could have rigged (for better lack of word) my phone to create such a long list?

Answer: 
The term is "phone number spoofing". It is quite easy to make calls from a phone number other than your own, this is usually done with VoIP software, although I don´t use skype either and I don´t know if skype has this capability. In other words I doubt your phone or the company is the problem.
You mention your "old" cell phone number. It is possible to "clone" a cell phone by making a different handset transmit the same identifying numbers as your own. That's easier to do with a CDMA phone, hence Lucas NN's question in the comments.

I'm not sure hat to tell you to do about this since you haven't really explained the problem that has (apparently) resulted. If your cell carrier is complaining, or perhaps trying to charge you, ask them to provide information about the geographic location from which the unknown calls were made. If you're lucky, it'll be different from where you live.

There's a short article on cloning here: <http://en.wikipedia.org/wiki/Phone_cloning>