There are Let’s Plays that I think are better than others, but I don’t think any of them, even the best of them, are popular enough to be part of gamer culture.
However, the gameplay video that I think comes closest to leaving “a mark in history” is this single video by pannenkoek2012: https://www.youtube.com/watch?v=kpk2tdsPh0A “SM64 - Watch for Rolling Rocks - 0.5x A Presses (Commentated)”. That’s the only video I’ve seen referenced in comments on videos of completely different games. The references are to “parallel universes” and “0.5 A-presses”, terms that are explained in this video. I don’t know if you could call this video a Let’s Play, though, since the commentary is recorded after the gameplay, it’s not part of a larger playthrough of the whole game, and the video has custom-made animations to aid in explaining the game, not just raw gameplay footage. It’s quite interesting, though, especially to a programmer.
Among popular Let’s Play series, one I recommend is the Achievement Hunter Minecraft Let’s Play series: https://www.youtube.com/playlist?list=PLA689F118656DB852. (Yup, they snagged the username “LetsPlay”.) In each episode, members of the Achievement Hunter group of players play some custom-made activity together in Minecraft. I don’t like the personalities of the players/commentators that much, but the immense creativity of the challenges and the players’ occasional funniness make it worth it. After 100 episodes it started getting repetitive though.
A few other lesser-known Let’s Plays I recommend:
• Cryaotic’s Undertale playthrough, Pacifist route: https://www.youtube.com/watch?v=kwPDQB0EVbY&list=PLeqwXTaiY-.... He is generally calm and empathic, which means he isn’t distracting and he roleplays a pacifist character well.
• After that, NateWantsToBattle and Brett Ultimus’s Undertale playthrough, Genocide route: https://www.youtube.com/watch?v=Q6kpGtgy3bQ&list=PL_IirJiXdc.... They add a sarcastic “don’t-care” layer of commentary on top of everything that makes the violence easier to enjoy without feeling bad for the characters who are killed.
• CarlSagan42’s playthroughs of online levels in Super Mario Maker: https://www.youtube.com/user/CarlSagan42/videos. He is better at the game than me, so he can beat levels that I couldn’t, and when he does a hard trick or glitch that is necessary to beat the level, he explains it for the watchers. Also, when a level does something interesting with the limited objects that can be used, he goes into the level editor and figures out how it works. He doesn’t throw a tantrum when he fails, and his video-end responses to watcher questions about science are often interesting, as well. The downsides of his channel are occasional Twitch subscriber banners interrupting the video, and Carl sometimes missing the obvious solution, which viewers call “Carl Blind”.
There are more Let’s Play series I have watched and enjoyed, but this list is big enough already.