Is there an age limit for a Skype account?

Skype

Yes, this is copied from the Skype Terms of Use

2.2 You cannot accept these Terms if: (a) you are not lawfully entitled to use the Software, Products and/or Skype Websites in the country in which you are located or resident or (b) if you are not of legal age to form a binding agreement with Skype.

In the U.S. the age would be 18 years old.