.. Well, this is a tricky question.
Trust the Well-Red Mage to come up with such a big subject! I’ve been gaming for quite a long time now, but I don’t know whether I’ve even played a game for each year of my life. Nonetheless, I’ll give this a bash – the rules are simply to post a game that came out in each year since my birth, and it’s my favourite one rather than the one I think was the best or the most influential or anything else. Since I can’t remember off the top of my head which games came out in which years, I’ll be using Wikipedia’s ‘years in gaming’ pages (which are fun to read through and just watch the lists getting longer and longer) and hope it doesn’t omit anything too important!
Check out a couple of the other answers to this question, by the way; I’m sure there are more, but I’ve recently seen Adventure Rules and Dragon’s Tea Party post responses which are probably much more betterly thought out-ened than mine.
This will make some people angry (at least, it makes people at my work angry sometimes), but I was born in 1994. So let’s get started! (By the way, lots of other peoples’ answers will have lots of images and full-on descriptions of each game, but I’m kind of pressed for time so I’m literally just going to list ’em. Sorry!)
1994. Donkey Kong Country
1995. Chrono Trigger
(Honourable mentions to Star Wars Dark Forces, EarthBound, Yoshi’s Island, Rayman and Worms. Good year, apparently!)
1996. Pokémon Red and Green
1997. Final Fantasy VII
1998. Legend Of Zelda – Ocarina of Time
1999. Pokémon Snap
2001. Crazy Taxi
2002. Kingdom Hearts
2003. Pokémon Ruby and Sapphire
2004. Spider-Man 2
2005. Kingdom Hearts II
(Sorry, Resident Evil 4 and Star Wars Battlefront II.)
2006. Final Fantasy XII
2008. Mirror’s Edge
2009. Batman: Arkham Asylum
2010. Civilisation V
2011. The Elder Scrolls: Skyrim
2012. The Walking Dead
2013. BioShock Infinite
2014. Pokémon Omega Ruby and Alpha Sapphire
2015. Rise of the Tomb Raider
2016. The Last Guardian
2017. Horizon Zero Dawn
2018. Kingdom Hearts III. Please.