Most phones, even those in law enforcement, are unable to glean any information from a call made by Skype.
Skype is one of many (and the best in my opinion) internet to landline phone communication tools available.
Often your number will show up like this (above) on a caller ID. This may look like it contains some sort of identifying information, but it doesn't.
It's easy to get Skype:
1) Just download it for FREE from SKYPE.COM (for both Mac & PC)
3) Buy Skype OUT credit (minimum $10 / calls in USA are 2.1¢ a minute)
4) Dial on the on screen keypad as you would a normal phone
5) Use your Mic & Speakers on your computer
You can also download plugins to mask your voice if you think your call may be recorded.
One side benefit to using Skype is that MOST states do NOT recognize phone call recording laws when the originating phone was Internet Telephony based.