On a per-call basis, I don't think there is a simple way to do that. You'd have to access your account's Caller ID settings, then disable Caller ID before making that call. You can't do this on the apps for mobile phones and other portable devices. I think you can do this on the programs that run on the computers, and definitely know you can get to Caller ID settings when you log into your account on the Skype web site (use the "Account" link at the top of this page to do that).
Even if you disable Caller ID, there may still be a number that displays on phones you call. This number won't identify you specifically, but may identify the call as coming from Skype. It may be a series of numbers that are not a phone number (for example, 0000123456 or something like that). This is something done by Skype's partner providing the connection to the telephone network, and Skype has no control over this.
Yes, true you can disable Caller ID by accessing your user account online.
This will block the display of your number but the username is still displayed.
Is there any way to hide your user name too. Your name showing up on a call
is almost worse if you want to remain anonymous.