Here are some greatly-known ones, primarily in arcades:

• Galaga. The ultimate refinement of early shmup design - before this there was Gorf, Galaxian and Space Invaders, all of which had good ideas but less happening for long term play. After this the genre took a turn towards scrolling games where more production values could be thrown at you. You can play Galplus or the other direct sequels, but it's more like different takes than improvement.
• Robotron 2084. Same thing as Galaga but for twin stick games which had a bit of ancestry in "characters moving and shooting" games like Berserk before Robotron, but didn't have it put together into the recognizable twin-stick scenario. The entire genre tries to glue more stuff onto the Robotron template, but it already has what is essential.
• Lode Runner, Boulder Dash. These are pioneers in "action puzzles on a grid with characters and level design", a genre of puzzle game which is hard to imagine not having now, and is essentially timeless. These two were directly preceded by "Space Panic" and "The Pit" in arcades, respectively, but it was on the home computers that these games found their refined and playable form.
• Sokoban. Sokoban, like Lode Runner and Boulder Dash, is a character puzzle on a grid, but with no arcade elements. Also timeless, though newer takes on Sokoban all add undo and other conveniences. Also worth mentioning with Sokoban is Pitman, which is like a turn-based Lode Runner. It had a nice visual update on Gameboy as "Catrap". (Early Gameboy releases are a reliable source of old games that people still craved a port of after 1989)
• Outrun. It's a simple arcade racer. Other games like Pole Position or Buggy Boy could substitute. But aesthetically speaking, the game is The One Everyone Remembers, definitely aged in its sprite graphics and FM sound but still a compelling vision of "driving into the sunset with your girlfriend", with no extra gimmicks like its 2000's sequel.
• Zork. A difficulty of exploring the adventure gaming genre is in how quickly it consolidated itself into genre tropes that emphasize niche forms of challenge. Zork, being one of the first entries in adventures, manages to keep it simple enough: there's a fantasy world to explore and puzzles and some random chance elements. The vocabulary is limited but doesn't strive to get in your way.
• Ultima 4. Roleplaying is probably the genre that is hardest to make recommendations for since it's gone through so many fashion trends. I pick this particular one as opposed to any other in the series because it hits a nice balance of conveying a unique roleplaying world and quest style(follow an ethical code to become an Avatar) versus being a simple and playable experience. Ultima never emphasized combat or grind although it has a little bit of that going on, which makes it unique among most 80's RPGs since the easiest way to pad out these games is to add punishing grinds and gotchas. Earlier Ultima entries are just simple(3 in particular still quite playable), later ones become more burdened by worldbuilding(5 is still worth trying if you want a challenging, sometimes confusing quest). The NES version, though not "authentic" to how the original Apple II game looks and feels, is probably the most accessible port of it. All the Ultima games rely on basic conventions of the genre during this period: write down all the dialogue for hints, make maps of each location. The puzzles are loosely structured and can be sequence broken by knowing what keywords to type or where to search.

And some lesser-known ones:

• Bill Williams' Alley Cat and Salmon Run. Two arcade games that engage with the lives of the titular animals. Relatively simple but creative and fun to play every time.
• Xagon. An arcade game for the Atari computers styled after the more popular arcade hit Q-Bert, this game uses hexagons instead of cubes and its sense of graphic design still works perfectly.
• The Return of Heracles. The approach to role playing in this game is really noteworthy since it figures things like a kind of board game - there is a lot of RNG, a lot of puzzle solutions that will get your character killed, forcing a new one to take their place - and you are expected to roll with it. When people say 80's games had teeth this is a good example of it. That might sound bad, but it's the same kind of tangible risk that made battle royale games blow up in the 2010's.
• Journey to the Planets. This is a game played because it is hyper abstract in the ways that only early 80's games were - the scale of objects, the vague representationality, the flashing colors and strange noises that only Ataris could do. The sense of raw experiment shines through this game, and while you'll probably become frustrated and give up very quickly, it's about the look and feel. Zelda came along and made things boring.
• Alternate Reality: The Dungeon. This was a high-minded, overambitious roleplaying project that got to its second game before giving up because of publisher issues. What's special about it? The depth of simulation, mainly. The first game, the City, had weather effects, diseases, alignment, reputation and seasons, but it was a kind of prelude to the Bethesda-style open world in that there were few explicit goals. The Dungeon added in a traditional questline chain, and explored the worldbuilding (a "kidnapped by aliens, forced to participate in a fantasy simulation" premise) in much more depth. If you are going to play one first person dungeon crawler from this period, this is the one I'd go with. It shows its age, but the atmosphere remains striking and unique. One of the first major encounters in the game is your doppleganger, who mirrors your own stats. You can get sick with the "Crystal Death" which makes you stronger but slower until you freeze. If your inventory is full, "The Devourer" will arrive to reclaim memory by consuming your items. The game has big ideas conveyed in a simple way, and the interface only has a few things that take effort to learn: you can get down to the business of grinding, mapmaking, hint collecting and puzzle solving pretty quickly.
• Project Firestart. This is one of those games that occasionally appears on lists of predecessors to modern survival horror. It's a very fully realized, cinematic take on how to do the genre, despite being stuck in side view and requiring disk swapping to move around the sci-fi, alien-infested ship. It was made for the wrong machine, TBH - it would have blown away a lot of people on Amiga or Genesis. The C64 graphics make it a little weaker aesthetically than it could have been. But I wouldn't call it obtuse or unplayable at all.