Popular games that "hold up" in the long run are usually those that paired a unique gameplay development with superb polish. The ones that don't are the ones that relied on graphical flash or some sort of other gimmickery. Even though I loved the arcades of the 80s and 90s, they admittedly were a carny place, and graphical flash was the order of the day. So not a lot of arcade games hold up as classics that people want to go back to.
The biggest crop of those that do actually seems to be among the earliest releases. Right around the early 1980s, when technology had advanced a significant step past the initial monochrome primitiveness of Pong, but was still sufficiently limited that designers had to come up with something that was actually fun and compelling to get people coming back for more.
Pac-Man burst onto the scene in 1980 as a quirky, colorful alternative to what had thus far largely been a crop of grim spaceship games with little color. Don't underestimate the power of the aesthetics here. The game's clean, simple lines and use of contrasting color (that is as vibrant as 1980 chips were going to get) still look pretty good today. Paired with the well-conceived sounds kicked out by the surprisingly potent Namco Wave Sound Generator chip and you can see why the game charmed the pants off of people then and is still appealing now, lending itself well to casual phone and portable device play.
Namco had this thing in the early '80s about releasing a rough first version of a game, then releasing a more polished sequel extremely quickly afterwards, usually with the sequel completely outshining the original (New Rally-X, Galaga, etc.) Pac-Man actually followed this pattern too, though the original was actually more financially successful than follow-up Ms. Pac-Man and stood up on its own better. But a detailed look at it does show that it's a technically inferior version of the game.
The main issue with it (as compared to Ms. Pac) is that there's only one maze. The game does get a lot of mileage out of giving each of the four ghosts their own basic AI script, but players can still fairly easily find and exploit patterns with a little play, with the only difficulty increase between levels being that ghosts launch from the base faster initially, move a little faster, and the effects of "power pills" grow shorter. The ghosts wouldn't have a true element of randomized movement introduced until Ms. Pac-Man, which also added cycles of four unique mazes.