Roughly in order:
Fallout (and Wasteland which inspired it)
The Old Republic (KOTOR 1-2 much, much more than SWTOR)
Vampire the Masquerade: Bloodlines (Word of Darkness) -- sadly we're getting an MMO not a sequel 🙁
Elder Scrolls (despite the weak main quests)
D & D (especially Planescape)
Mass Effect
Borderlands (Pandora)
Saints' Row (much more fun for me than GTA's sandboxes)
Mass Effect is the best, no question.
Borderlands - interesting that you've suggested that one, OP. Having played both, I'm a fan of the gameplay of the BL series, but the universe is nothing special. I felt the characters added the character to the game, rather than the setting. Not so with the Mass Effect games. There, the universe created an often emotional experience that was incredible (yes, I do like the 3rd game).