In reply to ClimberEd:
Changing your password is very likely to be sufficient.
If you visit live.com, log in using your Skype username and navigate to the security options you can:
- Check that other security details they have for you are correct
- See where else your account is logged in
- Optionally, set up two factor authentication to make your account more secure in the future
Two factor authentication will be a bit of a hassle if you often log in on new computers but probably worth it if you hardly ever do that or your Skype account is important to you professionally.
The most likely way the spammers got access is by the release of passwords from another site where you used the same email address and password.