This one pretty much writes itself. The Godfather is a hugely popular franchise, but I guess it might have a more niche appeal than many of the other choices in this list. The last film came out in 1990, almost 30 years ago, and the two games that came in the past decade were good, but didn't sell huge numbers. That being said, I think The Godfather would be an amazing fit.
So much like 2006's The Godfather on PS2, I imagine playing as a brand new initiate who must rise the ranks in Don Corleone's "family". You would go out and interrogate perps, persuade shop owners to give protection money, manage various rackets, and, of course, whack some dudes. All while dealing with the pressures of being part of a crime syndicate.
If you've seen The Godfather, or any gangster flick, you can see why this would make for a thrilling video game. Imagine the web of lies you would have to manage in order to stay one step ahead, and the horrible things you would have to do in order to ascend. Once again, it writes itself.