Sure you can get notice.  Sign-in to geocaching.com then from your 'my cache page' click on edit profile (the link is right next to My Account Details in the top left area and then check the box for 'send me a weekly emailer...'
 
MO & GO

David Thompsen <dthompsen@yahoo.com> wrote:
It isn't. :)
 
There was a free utility out there that would email you when something new hit your pre-determined radius, but after some programming changes on Geocaching.com a couple of months ago, it no longer works.
 
I believe that new cache notification is a "coming-soon" feature of premium membership, though when that may be implemented remains to be seen
 
Team Cow Spots

SquishyGecko <squishygecko@yahoo.com> wrote:
So I've looked all over the website and can't figure out how you have the
site notify you immediately of new caches in your area. How is it done?


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