The Calendar control included with ASP.NET uses postbacks only. If you added Microsoft ASP.NET AJAX to the page and put the calendar into an UpdatePanel, it can reduce the appearance of postbacks by using callbacks. But it still makes a trip to the server for each click on a date or month.
Many people have created replacements to the Calendar control that uses javascript to do the work. I am the author of one, in "Peter's Date Package". You can locate others in these sites: the Control Gallery (here under Resources), www.123aspx.com, and www.411asp.net.