1996: We got a PS1 in 1996 which, looking back now, seems to be when a lot of the big hits came out. We got Crash Bandicoot, Resident Evil, Tomb Raider, Wipeout, and Die Hard Trilogy, but other than that I believe we just rented everything from Blockbuster. Plus, I remember buying every single PS1 magazine with a demo disc. I practically lived on demo discs back in the day as a child. My favorite PS1 games, though, were easily Ape Escape and Metal Gear Solid (the latter of which I would play with my brother, I think I was too young to really understand the game mechanics and the convoluted story).
1998: In terms of my own games I was playing Pokemon Red on Gameboy. Played the absolute shit out of that game. Other than that, it was the year our family got our first proper PC (with voodoo gfx I believe) for Christmas. My two older brothers had totally different taste in games - one got Commandos: Behind Enemy Lines and the other got Rainbox Six. I was the youngest so our dad let me choose which game we would play first. What followed was my two brothers bribing me with different sweets and fizzy drinks so that I would pick their game. We ended up playing Rainbow Six but I actually preferred Commandos. I was young at the time and I couldn't quite keep up with all the menus in Rainbow Six.
2000: Fucking PS2 babyyyyyyyyyyyyyyyyyyyyy. I remember renting ESPN Snowboarding and being absolutely fucking floored by the snow particle effects. I also clearly remember how we bought Zone of the Enders for the Metal Gear Solid 2 demo disc and ended up only playing ZOE once before trading it in for something else. Funny thing was the independent game shop we usually went to said that ZOE was practically worthless without the demo disc because the latter was what people really wanted (they were actually selling the demo disc standalone - probably weren't supposed to be doing that but things were lax back in the day).
2000 (still): FIFA 2001, baby. The graphical leap was mind-blowing at the time. Online wasn't a thing but my brother and I would play co-op tournaments on the weekend. Luckily my brothers were still spotty single teenagers with no romance prospects so I wouldn't be on my own playing games.
2001: Seven words. Metal. Gear. Solid. 2. Sons. Of. Liberty. That is all, thank you. Oh wait, also Grand Theft Auto 3. I think those were pretty much the only games I played for that entire year.
2002: Got a Gamecube and played the shit out of Wind Waker (but not much else to be honest, Gamecube was just a Wind Waker machine for me). Fun fact: my parents refused to buy the game and insisted I had to rent it, but I had them rent it so many times that it would've been cheaper to just buy the game anyway. Medal of Honor Frontline, GTA Vice City.
2003: Max Payne 2, Need for Speed Underground (get lowwwwwwwww get low get low get low get low - through the windooooooooooooooooooooooooooooooooooooooooooooooows, through the wwooooooooowlllllllllllllllllllll)
2004: Rise and shine... Mr Freeman.... World of Motherfucking Warcrack Warcraft, Far Cry, GTA San Andreas, MGS3, also ended up playing shit loads of Counter Strike Source.
2005: Battlefield 2, Call of Duty 2, Brothers in Arms, F.E.A.R., Guild Wars (because my parents would keep paying for my WoW subscription lol), TimeSplitters.
Comment: I think for me (ie my personal tastes), 2005 was the last real heavy-hitter year for games that blew me away. The years that followed of course have some great games but I don't think any them topped what came from 1996 to 2005. Those are the golden years for my lifetime (older folks will probably see it differently but this is my personal history).
2006: Company of Heroes, Ghost Recon Advanced Warfighter, Rainbow Six Vegas, Project Gotham 3, Dead Rising, Elder Scrolls Oblivion, Gears of War.
2007: Crysis (I thought it was a shit game but visually very impressive), World in Conflict, Call of Duty 4 Modern Warfare (this was the only game to overtake BF2 as my preferred online shooter), Stalker (super confusing game coming from majority of games that had tutorials or at least eased you into it, Stalker was just brutal and I never got much further than the start of the game), Halo 3 (the last good Halo game IMO).
2008: Grand Theft Auto 4 (the ragdoll physics were amazing for the time), Rainbow Six Vegas 2 (felt like this was the first game for me with over the top collectable skins etc., precursor to everyone charging for them many years later), Battlefield Bad Company (good game with cool destruction but I didn't like how clunky it felt compared to BF2, I imagine it would've been good on PC with higher mouse sensitivity but alas it was console-only), Warhammer Online Age of Reckoning (I love Warhammer so I was super happy when it launched, also enjoy the public quests).
2009: the year I went to university so I didn't play as many games, but I did (with my flatmates) play the shit out of FIFA 10. Also played a lot of Call of Duty MW2 (I must've played the Russian invasion levels hundreds of times).
2010: FIFA 11. Nothing else really stands out in my memory. Bit of a boring year for games I might be into.
2011: was out of the country for 2011 with no access to my gaming PC or consoles, but looking back it doesn't seem like I missed a whole lot other than Battlefield 3.
2012: Total War Shogun 2, WoW Pandaria (tried it got bored quickly), another pretty boring year for me.
2013: Definitely Battlefield 4 (played it online day and night) and then GTA V.
2014: Played a lot of COD Advanced Warfare. I liked having Kevin Spacey as a villain. Also enjoy Infamous Second Son. Ah yes and I spent weeks being amazed by Driveclub's visuals. Cannot believe what they achieved back in 2014.
2015: Got hooked on MGSV for quite a while. Tried to get into Cities Skylines and gave up pretty quickly. Really enjoyed Life is Strange and Everybody's Gone to the Rapture.
2016: Uncharted 4 (awesome game, a good popcorn muncher), Fifa 17, Rocket League (was never very good at it but that didn't stop me enjoying it).
2017: Breath of the Wild by a long shot. Also really enjoyed Mario Rabbids. Xenoblade Chronicles 2 would've been good if it weren't for the dogshit voice acting. (you can tell this is the year I got a Switch).
2018: Honestly cannot think of anything I really played at any great length aside from Squad.
2019: Tried to get into Resident Evil 2 Remake but was too chicken shit to get very far. That's all I can think of, other than replaying Breath of the Wild and also dabbling in a bit of Mario Odyssey.
2020: I got Yakuza Zero and played that quite a lot. Not much else.
2021: Played a lot of Judgement (not Lost Judgement).
2022: Currently playing a lot of Metroid Dread.
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Wow that was a rollercoaster. Hard to tell whether 2005 really was the end of "the good times" or whether it's just when my interest/love/time for video games peaked. As you can see, fast forward to 2022 and I hardly play anything.