I remember feeling quite overwhelmed when going to Stonehenge. It wasn't a feeling of sadness, more something like what a Romantic poet would call "an encounter with the sublime". I hadn't expected the stones to be so big and overbearing. This would've been a little over 20 years ago, when I was in my late teens.
I've been to many stone circles and the like over the years, mainly in Ireland. I've never felt the same effect anywhere else that I've had at Stonehenge, in terms of ancient sites. It's usually just a feeling of wistful mystery and loss (like another post described).
The most intense reaction I've had to anything "tourist-y" was seeing Picasso's Guernica in person for the first time. I cried my eyes out at that. Again, like Stonehenge, I went in "unprepared" without much expectation and just found the sheer *size*; of Guernica overwhelming. Maybe that's a clue as to why these ancient sites provoke such reactions in us sometimes.