Yeah, add me to the Alpha Protocol bandwagon. In fact, I defended this game since day 1, and 2/5 review on the Escapist. 7 full playthroughs, platinum trophy and loads and loads of fun with exploring new ways to solve the problem (ending the game with Steven Heck on a boat - priceless).
From much, much less obvious spectrum of this topic -
Pathologic. Russian game from... 2005 I think. Weird, confusing, but also intriguing story of three completely different people trying to solve a mysterious plague in a rural Russian village, each one with different skillsets, events (which WILL happen, regardless of you being there to witness them, it's an "open world game" with a 1 second real time = 1 minute in game), and even allies/enemies in the town. Add to it a great survival mechanic, when you have to manage budget for food (the prices skyrocket after the plague hits), water and medicine, as well as trying to avoid getting infected in the diseased districts. And if you'll get infected... Then you can't cure it, and have to take care of yourself even more, to not die from it, while still going forward with the case.
Awesome concept, which I really enjoyed. But, since I'm talking about it, it was obviously bashed by the critics. Why? Well... Because it looked like this:
It also sounded like this, it was animated like this and melee/ranged combat was also as crappy as this picture. In fact, things I wrote in a paragraph above are the only redeeming factors. If there's any game that really NEEDS and HD, polished remake, it's this one.