Have you tried the Blackwell series (can be found on Steam, GOG, Desura and probably some other storefronts). It's a series of adventure games set in modern time, with supernatural elements. I quite enjoyed it.
While not exactly new, I would also recommend the first Mafia game, which had an excellent story. (Don't know where it is sold anywhere these days, but a boxed copy should be easy to track down, the game sold relatively well)
Papo & Yo is a rather short puzzle/adventure game with a very touching story. It's not a grand sweeping one, but rather deals with more human problems. I won't spoil anything, but I found it to be one of the most touching games I've ever played. Can be bought on Steam & Humble store.
Thomas Was Alone (steam) might look like an incredibly simple game, but it has a strong story, and its simple aesthetic design is worked into the story.