It's impossible to pick out just five of the most important games ever, but I'd try to pick games that have important historical significance, have some degree of genre diversity, all while still being fun and thought-provoking games you'll always want to pick back up.
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Ultima IV.
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The first RPG that wasn't a giant dungeon-crawling grindfest where you slay a wizard at the end. It has a big open world, fun NPC interactions, and fun tactical RPG gameplay for the time. Has a really good philosophical storyline that is integrated with the game mechanics, and it shows how creativity can form under constraints. Another good option would have skipped to the SNES era with Final Fantasy VI, which is slightly less retro but is more approachable and has an equally compelling story with stronger replay value and tons of mods/romhacks. -
Resident Evil 2.
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One of the problems with choosing only five of the most important games is that the horror genre and the point-and-click adventure genre both are important in the history of gaming, but there isn't room for both. Resident Evil 2 blends both genres exquisitely in a really compelling, but also endearing B-movie story with lovable characters. The Walking Dead would have been another option, but it doesn't really have gameplay and it strays far enough away from the adventure genre that it doesn't serve as a good example. -
Flower.
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The Indie Revolution was an important era of gaming history, and motion controls were really big back then. Beautiful, subtle story about overcoming depression. Roger Ebert was wrong and video games could be art. Any indie game during the Indie Revolution golden era (August 2008-September 2015) would fit here, but I picked Flower because, at the time, it challenged what people's expectations of what a video game was supposed to be. Games don't have to be challenging or about fighting to be legitimate. Doesn't have a ton of replay value, but it's the sort of game you'll always come back to during hard times. Barely beat out Stardew Valley, which is longer and has more replay value but isn't an "art game," which was very much the zeitgeist of the era, and Celeste which, in addition to having a beautiful ludonarrative story like Flower, would have also been a good mascot for speedrunning communities, but was created post-indiepocalypse and therefore isn't a good example of the era. -
Nier Automata.
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A really engaging action-focused game with a good story and tons of replay value. Bloodborne and Bayonetta would have also been good choices, but I ultimately went this one because you'll spend more time on it, and there's a co-op mod. It does make this list RPG-heavy, but it's hard to find a pure action game with as much replay value and attention to the plot. It's still a skills-based game and none of the RPG mechanics will save you on the hardest difficulty. -
Baldur's Gate III.
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I would put an open-world, choice-based game here. Even though BG3 is not a true open-world game, it has many the sandbox features open-world players like short of a fun physics system. It's the third entry in the series, but the game doesn't expect you to have played the first two games. Great mod support. I didn't choose other popular open-world/open-zone games because many have paper-thin quests that lack player agency (Daggerfall, half of Oblivion, Skyrim, Dragon Age: Inquisition, Breath of the Wild), don't work as a standalone experience (any of the Mass Effect Trilogy, the Witcher 3), are amazing but too small in scale to be good representatives (KOTOR, Dragon Age: Origins, Deus Ex), are too controversial (Grand Theft Auto, which railroads you into being a bad guy) or have a strong open world and player choices but terrible gameplay (Morrowind). I gave BG3 the edge over Cyberpunk and Fallout: New Vegas due to built-in co-op and endless replay value that would last a lifetime.