Asterisk can use analog or digital (IP) phones, and can use analog or digital (IP) phone lines.
Or, you can use a mix with somebody like Vonage: You send digital data to Vonage, and Vonage sends it to an analog phone line at the far end.
If you have an IP-capable phone at the other end (either hardware or a software phone), you should be able to send digital calls for free across your IP (Internet) connection.
Of course, you've been able to do that sort of thing for years with software like NetMeeting and even MSN Messenger, too. You don't need an Asterisk box to make "free" phone calls. Asterisk comes in handy with its ability to convert many phones of many different types, and to route calls, share lines, etc.