STALKER: Shadow of Chernobyl.
I'm amazed this one didn't get many mentions.
Protecting a wounded friend from a pack of hungry dogs with naught but a pistol, a knife, and a grenade which I can't use because a shrapnel might hit my friend. I manage to fight off the dogs, but I don't have a medkit. So I trust him to survive, and go to find someone willing to trade a medkit away. I search for about an hour, but no one I find has a medkit to spare. I go back to my friend, but he's not there. Suddenly, I'm attacked by a pair of boars! One flees, but I know I can sell boar hooves for fairly good money, so I pursue. On my way, I pass over a corpse in the boars' lair. I dispatch the boar, and go back to see what the dead man has to offer. It's my friend.
I'm traveling, and I'm becoming increasingly hungry. I forgot to buy some bread back at the village. I come up on a camp, but I know people in the Zone don't trade away food. I sit there, let a man finish his song on his guitar, pull out my pistol and put a bullet between his eyes. The other two people freak and pull out their weapons! I retreat behind a tree for cover, and take out the other two after a short gunfight. Food enough for a couple days.
I'm traveling again, trying to get to the bar, my normal path is currently being traveled by a large group of bandits, so my only other choice is through a valley home to a very large pack of dogs, there's so many because people usually take the other route, so no one ever bothers them. I take out the biggest, scariest gun I have, and trod ahead. When the dogs start to rush at me, I open fire in their general direction. The gunfire frightens them, and they run away, all but one, one I hit. It's behind the pack, limping desperately away from me. I look over toward the bandits, hoping none of them were alerted by the gunfire. They are all looking around, looking for cover for the potential fight. I duck behind a bush and wait for them to dismiss it and walk on so I can get to the bar.
And the broken english, which does so much to help it, but probably is due to mistranslation.
And none of it's scripted, so it's impossible to know what's next and there's always something to do.
EDIT: It's also the only game to make me want to know the history of Russia and to delve into learning the Russian language (which is incredibly easy to learn).