On a more ethically questionable note,
infiltration, where the site being explored is still active. I could have been arrested a couple times doing this one. Once, a few of us went up 43 flights of stairs in a neglected stairwell of a skyscraper to reach the top floor and see the view. We were spotted on a camera so they were ready to laugh at us and send us back down when we finally got to the top. This was pre-9/11, so they were more forgiving of such things.
I have explored abandoned places too though, including the foundation of an old water filtration plant. The top was totally destroyed and they were getting around to clearing the rest of it, but there was a huge network of concrete tunnels, partially underground, complete with the usual homeless encampments etc. Then you have your usual construction sites, warehouses, and so forth. You really do have to be careful doing this though, the dangers are real (talked a couple people out of exploring an old school because of the abestos thing... it's a shame, because I bet that place is beyond creepy-cool inside).