In terms of copies sold, Generation I was the most popular, hitting over 47.5 million. After that came Generation II, at 29.5 million. Sword and Generation VIII came next, with 21.1 million sold as of March 2021. No Pokemon game did badly (unless you count LGPE's relative failure), and as such, all are popular.
Experts and game reviewers are not the best source to determine what games are the most popular (They think Sword and Shield are average/good, but more vocal fans express hate, some considering them the worst of the series.). Fan input is more reliable, so I'll be going with common consensus I've seen throughout my years of playing.
Gen 1
Considered "the gen". Genwunners are the people that consider Gen 1 the best of generations, and as there's so many of them, the games are clearly popular. Gen 1 was a lot of peoples' childhood, and the nostalgia plays a big part. The only things that bog them down are the less-than-modern capabilities of the 1990s, and as such the games are glitchy, buggy messes filled with poor choices.
Gen 2
Extremely positively received, as old fans got to take on Kanto again and new fans being drawn in for the first time. Criticisms were mainly directed towards a poor level curve and lack of variety in Pokemon, but overall, Gen 2 was a hit. It attracted fewer people than Gen 1, however, as evidenced by the sales -- so for all its praise many people still deemed Gen 1 superior.
Gen 3
A success, but people didn't like it as much as the first two generations. The main reason is because you're unable to transfer Pokemon from Gen 2 to Gen 3, meaning your Level 100 Charizard you raised in the '90s isn't able to follow you to Hoenn. Other reasons fans drew on to dislike the games were the amount of legendaries they brought: ten was a massive step up from the last generation, making people feel as though the legendary status was being diluted. The games were appreciated, however, for the unique concept of two villainous teams (fighting both in Emerald), the Emerald Battle Frontier, and massively popular Pokemon like Blaziken, Swampert, Gardevoir, Flygon, and more. People generally liked Emerald more than Ruby or Sapphire, due to more gameplay and a Battle Facility. Overall, they were popular games, just definitely not the most popular Pokemon games.
Gen 4
What many players consider the absolute best generation. Diamond and Pearl were decent, but then Platinum came and blew them out of the water. People loved Sinnoh, and they still do. The biggest reason Gen 4 was so popular though, is because of HGSS. Games from a kid's childhood were being remade into something bigger and better, with more vibrant colours, moves, Pokemon, and more. The terrible level curve was still in place, but Pokemon variety was improved, and HGSS were even better received than the first Johto games.
Gen 5
Hated on release, beloved by the fans now. The fanbase's hate for Unova was based on many things, including how "Game Freak had run out of designs" (Chandelure, Garbodor, Vanilluxe), and how only new Pokemon were able to be used. Despite this, they still sold well. At the time, however, they were the most hated Pokemon games out there. Black and White 2 were released, and fixed some of the "problems" with the originals: more of a story, and old gen Pokemon before the post-game. They were received better than the first ones, but "Unova bad" mentality stuck with people for a long time. In recent years, however, fans that grew up with Unova instead of Kanto are becoming more vocal, and Unova is recognized as part of Pokemon's Golden Age, up there with Generation 4.
Gen 6
The switch to 3D, while impressive, was not a good generation for Game Freak. Fans felt Kalos was bland and uninspired, the evil team was terrible, and Lysandre was just sexy Cyrus. People didn't appreciate the switch to friendly rivals/friends, either. The games sold well enough in their own right, but the backlash was strong, and many still find Gen 6 one of the low points of Pokemon to this day.
ORAS weren't as negatively received, but many fans still felt they cut corners. People hated the fact that they cut the Battle Facilities, and reviewers like IGN docked points for "too much water". Much like the original Hoenn games, however, they were still popular, even if complaints were voiced about the games being too easy.
Gen 7
Lots of problems here. You could barely progress without being stopped by Hau, Lillie, Kukui, or one of the other NPCs in an overly long cutscene. Festival Plaza was terrible in the eyes of many, a massive step down from the PSS just a generation before. Ultra Sun and Moon made the games a bit harder, and many fans appreciated it for the first modern Pokemon game with a challenge. However, they still aren't nearly as well-respected as the earlier generations, and as such Generation 7 falls down the list.
Note: I'd mention LGPE, but those were the worst sales ever from a mainline game and it's basically just Kanto. Moving on.
Gen 8
The most controversial Pokemon games ever. Dexit was a massive upheaval in the "Gotta Catch 'em All" mentality of Pokemon, and many fans expressed desire to boycott the games for such injustices. attitudes didn't get better when the games released, either -- models were taken from the 3DS games, animations were shoddy (look up Double Kick Generation 8 and laugh), the map was linear, the story was nonexistent, trading and battling online weren't free and there were far too many cutscenes for most peoples' liking. The games are the third-bestselling Pokemon titles of all time, but the vocal minority hated on them to no end.
So, to conclude. Generatons 4 and 5 were considered "The Golden Age of Pokemon" by many, and Gens 1 and 2 were no slouches either. The general order of popularity based on fan reactions and sales should look something along the lines of:
4 = 5 > 1 > 2 > 3 >> 6 >> 7 > 8
Hope I helped!
