Darklands is a very unique RPG that I recommend for everyone to try. It has lots of mechanics that are just not found in the other games. At first it seems that you really have no main quest but you can stumble onto it after a while. Your guys have to deal with effects of combat and aging. Weapons and armor have just two stats: weight and quality - and those tell how effective the item is for the job. Somebody wants you to take out a robber baron? First visit the towns near the barons castle so you can get the reward from multiple places. Then you have to decide what to do. Do you attack the castle gate directly, siege the castle, talk your way in or silently during the night climb the walls? You can even try to pray for divine aid. Depending on choices you then can fight your way through the castle, during dinner challenge baron to a duel, try to persuade him into abandoning his criminal ways or when everybody is sleeping, quietly set the whole damn thing on fire.
Original Xcom is still a good game and in a ways more deeper than the remake.
Edit: Since definition of "old games" is looser than I previously thought, I can add games like Dead Rising to that and I have on going playtrough as an evidence of that.
@bradbrains: My Xbox 360 is not going to last forever - if there is piece of tech that plays those games, I am interested on it. Like everything, it is value proposition, right now there is not a console out there that has enough exclusives for me to buy it just based on that. Xbox One games + backwards compatibility comes close for being good enough deal to get one.