Unless someone is looking over your shoulder when you log in, or unless your computer has been hacked, no one can see who your Skype contacts are. Even if you adjust your privacy settings, Skype does not provide an option for making your contacts visible. You can, however, let people see the number of Skype contacts you have. You can also share your contacts with other Skype contacts while on a call or instant message conversation.
Sharing a Contact's Details
To share the contact details of one of your Skype friends with another friend, you first need to initiate a Skype call or an instant messaging conversation with the person you'd like to receive the contact information. You can then click the "+" button and select "Send Contacts." Type the name of the contact you want to share and select it from the list.
Showing Your Number of Contacts
If you want people to see how many contacts you have, you can share this information on your profile. All they see is a number beside your profile name. Your options are to share it publicly, share it with your contacts or keep it private. To change this privacy setting, select "Profile" from the Skype menu, click "Edit Your Profile" and select "Show Full Profile."