One thing you can do is to go here:
https://selfsolve.apple.com/GetWarranty.do
then input your Mac's serial number (which can be gotten from System Profiler - in your Utilities folder, also accessible from the About this Mac window - More info button, also accessible by option clicking on the Apple Menu).
From the resulting web page you can see what your current warranty status is.
I can't seem to find a way to get a hold of the purchase date directly. Yet.
charlie