Games where you can go Exploring

[11killer11]

I know i'm not the only one.

Are there any games out there besides missions and storyline driven that you could actually just explore the land (being cities or anything else for that matter)? Besides the obvious ones such as GTA: San Andreas, Ico and Shadow of the Colossus. I don't care if their first or third person view.

I bring this up because I'm researching Deus Ex for the PS2 and it just brings to mind that some games are not (you have to take this path) games.

EDIT:
I'm probably not that clear at the moment so let me explain it a little more. I mean a game where you can just walk around and see how things react to certain situations, see if things are breakable or not, see if you can do something that wasn't intended to do, find something odd.