This doesn't necessarily mean the best game you've ever played, just one that you thought about and pondered for a while after you played it.
For me, it'd have to be the (obviously) Assassin's Creed series, or Red Dead Redemption.
Assassin's Creed solidified an already huge desire to learn about history in general, with an added focus on the architecture. I love architecture, and the way you interact with it is essential to the basics of the game. Ever since the first game, I've been fascinated with architecture and how it works in relation to math and physics.
Red Dead Redemption took my love for the western genre and wrapped it up with my favorite medium: games. Nearly every facet of the game was executed to top-notch quality. The story also spoke to me with it's complex themes and underlying tragedy, even through the comic relief. I was left contemplating the story for a long time afterward, and even wrote a paper on it, which helped me ace a project in school. Also, the Undead Nightmare DLC didn't hurt either. I'm a huge zombie fan.
Thoughts?
The only game that has caused me to think of it deeply is Assassin's Creed. It came out when I was really questioning my religious beliefs, so the ideas it sparked in me made a lot of sense and finally pulled me in by the climax. AC2 gave us more personal issues the character had to deal with, which drew me in even more. To this day, the story always gets me thinking.
Assassin's Creed. No other game has made me, an atheist with no attention to the past, look up matters of religion and history. After playing AC1 I read the Torah, Quran and Bible. I researched Masyaf, Acre and Jerusalem as well as Damascus. After playing ACII, I did some research on the Papacy and all that good stuff. Just.. Such a mind blowing series. And most recently with Revelations, my mom is Turkish, she knew a LOT of the stuff in that game. It was a very enriching experience for both of us.
Definitely the AC series. The historical pieces are amazing as well as the conspiracy possibilities that are tied to most of the prominent people throughout the last 2,000 years. It's crazy to think that there is a possibility, however remote, that the majority of powerful people throughout history could have been tied to a two-sided battle that eludes the majority of the public.
Every time I play a FPS like the Modern Warfare games or a James Bond game, I think about how much "fun" it would be for a battle to break out in an every-day situation or to be a secret agent looking for a target in my office complex. Not "thought provoking" in its truest form, but definitely "day dream provoking".
Definitely AC series because I've always loved history and wondered what it would be like to be in those times. The games are actually a bit like it!
But at the risk of sounding like a broken record (an old-time music delivery system for all you young 'uns ), I have to say Shadow of the Colossus as the game which got inside my head more thoroughly than perhaps anything else ever has. It's magnificent but mysterious art that you can't help but think and wonder about.
Assassin's creed, after playing i started looking into secret societys thinking it was a big joke. come to find out they exist, AC has made me realize just how corrupt the world really is.
Metal Gear Solid, probably MGS2
Metal Gear Solid, probably MGS2
Oh yes. I forgot about that one. That whole thing where the AIs are just trying to prove to us that humanity isn't worthy enough to control itself. The freakiest thing? You can't ACTUALLY say that they're WRONG. All of the AIs arguments are fully sound, it's crazy. Here's a neat video of an analysis (fishes around to see if he can find it)
I have seen it, plus I replayed the game like 30 times now so I know the story pretty well.
I like how they analyze what a self is to Raiden, how most of his actions are self serving. The truth part was good as well, when things get bad ditch the truths we once had and replace them with more self serving truths.