Well, as Nostalgic as I might get here I should note that I suffer burn out or the "I have nothing to play" mentality from gaming rather often. So even those games closest to me are those I can only pick up if I'm in the right mood, so instead I'm just going after the games with the biggest impact on me. So note, this is
not quite a "Top/Favourite games" list cause I'm more going for the influence it had than how it stands a game overall.
Kotor, oh Kotor. This game did two big things for me, first it turned me from a Casual Star Wars fan to one a Serious Star Wars fan, changing my perspective of the series to be one of "That fun movie with lightsabers" to being a rich, deep and expansive universe. Secondly, it made me realize gaming was more than just a simple time killer. Biowares (former) way of telling a story, writing characters, the fact the game was far more influenced by dialogue and choices than simply combat. All of this made me realize what potential Video Games held as an artistic medium to not only engage people but to tell a story and leave people walking away with something.
Halo 3 was the video game that did two main things for me. First, it introduced me to the online gaming world where I didn't need to have someone over to enjoy jolly co-operation. Secondly though, it was a game that almost everyone played, so it acted as the bridge for my passion in Gaming to be shared among others and have it be respected rather than simply label me as "That Gaming Geek". Like, I was still known as that Gaming Geek, but Halo 3 let me actually share that experience with others.
With Kotor and Halo 3 being my two biggest games during my younger years (5-12), Mass Effect was the next step. I originally grabbed it under the impression it was just a hybrid of the two games I already held so close. But holy shit did it end up being more! Where Kotor was the Prothean Relic for how expansive gaming was Mass Effect was the Conduit. It's narrative levels blew everything else since out of the water (save for Telltales Walking Dead).
-----------------------
Everything else since hasn't had near the same level of impact on me, it may remind me why I love gaming but nothing else has had such a giant impact on me as how I grew up as a person. However, there was some
Honourable Mentions I have for games that still had a strong effect.
Pokemon
Like Halo 3, this game also played a big role in making my gaming hobby accepted by most other people. However, Halo 3 took 1st place in that regard because while Pokemon was more limited to School Recess Halo was something I'd then spend hours a day on creating a long list of memories. But the fact Pokemon was able to do it at a School level, and as a result make it more accepted to adults looking after us as well makes the series deserving of a mention.
Dragon Age Origins
Third Torch holder that Kotor and Mass Effect held beforehand, it continued to provide amazing story, characters etc. And was guilty of quite a bit of rushed/forgotten homework during it's first month out. However, in combination of that I prefered Mass Effects setting, and Mass Effect's sequels continued one consistent story while Dragon Age kind of... Well... didn't. It ended up being a fun and amazing play, but ultimately being overshadowed by Bioware's other title.
Tell Tales The Walking Dead
It's the fourth game to hold the torch that Kotor, Mass Effect and Dragon Age held in regards to amazing storytelling. In fact, with Tell Tale specializing on just that it managed to pull it off to an even higher degree. But, as a result it's also one of those Video Games that sort of sit's on the line where I'm positive in 10-20 years a new medium that's a descendent of gaming will exist, which Walking Dead will more accurately fit. But the reason it's just an honorable mention is because as great as a story as it had, that was it. I was already motivated enough with video games, and already comfortable enough with being a full out Geek that it didn't really do anything that big to my life overall. Though in the game's defence this is a result of time of release, not anything in the game itself.
Undertale
Yo! Spoilers are ahead!
This game was one of those cheap buys I grabbed in a "Let's see what all the fuss is about" deals. Since for the last few years Extra Credits got me in the habit of buying games that might not quite be good, but at the very least offers something unique so I buy and play it for curiosity and observations sake alone. Undertale ended up being one of those who had the delightful surprise of not just being a curiosity but an amazing as hell game in it's own right. Good writing and characters aside, it was it's more unique aspects that really made this game stick to me. Firstly the Mercy mechanic, this is one of a small amount of games that actively and consistently incentives and rewards you for being peaceful, as well as being far more engaging than simply fighting people. Secondly, it's Meta Mechanic. The way it takes a feature we take for granted such as Saving, Restarting and makes it not just another mechanic but an actual part of the universe? It was an insanely unique experience that left me both amazed and inspired to see what other games might take such creative angles in the future.
Dark Souls
I want to say this game introduced me to challenge, but that'd be a lie. Rather, it introduced to me the first game to make a remarkable understanding of making a game
challenging, but not punishing. It actively encouraged you to think about things, to plan, to strategize, to pay attention to everything going on in the battle. The game offers rich lore, music etc. as well, but it was it's rather beautiful execution of a challenge that not only rewarded player skill but encouraged and inspired growth I have yet to see in any other game that makes this an honourable mention.
-------------------------------------------
So yea, plenty more games I could list if I were just listing those I have fun playing. But as far as those with big impacts on me as a person or my perspective of gaming? That's pretty much all the main titles.