Notification Center is without a doubt my favorite Mountain Lion feature, particularly the way Calendar reminders go from moderately disruptive to not disruptive at all.
My favorite unadvertised feature is that you can now add files to the Trash while it's emptying! I know, it's the kind of thing that seems like a no-brainer/should have been there for years, but it wasn't.
This is great for me since emptying build folders, or large batches of icons takes a few seconds, and I frequently find something else to trash after I've already started emptying the trash.