Perhaps this is speaking the obvious, but as far as Gen I is concerned the answer is Pikachu. Possibly the most recognisable fictional character in the entire world right now, there's no competition here. It's literally on-par with Mario and Gollum, which isn't something Charizard or Mewtwo can make claim to (who I believe are 2nd and 3rd place). Gen 1 - Pikachu
Gen II is perhaps more difficult because it's kind of an extension of Gen I. They didn't create a Pokémon to be particularly iconic in wider society because the series was meant to end after these games. Within the Pokémon community, though, I think we have 4 contenders: Ho-oh, Slowking, Unown, and Pichu. Ho-oh for no reason more than for appearing in the very first episode of the anime before it was ever available in games (or even known by name). This granted it a huge amount of mystery and hype. However, I believe that that original burst of popularity hasn't necessarily persisted. On the other hand, Slowking has remained fairly popular since its feature in the 2nd Pokémon movie, in part because it's one of the best films, and in part because the Slowpoke line has received consistent top-ups to popularity since. Slowpoke has received its own song fairly recently, and the item SlowpokeTail has appeared in most games since Gen II, with it even receiving its own location in that generation (Slowpoke Well). Unown is a key character in all Pokémon lore as well as key movies such as the third one. It receives its own location in most games, and often there are rewards for collecting every form. However, this perhaps makes it only more iconic among the more dedicated fans who are interested in those rewards and don't simply play through the story and, even then, some of that fanbase find Unown tedious. Finally, Pichu is probably the answer I would give. It's been in 2 Super Smash Bros. games which gives it an inherent degree of iconography within the wider Nintendo community, and it has received some favouritism within Pokémon such as with the Pichu Bros. anime shorts, the special Spiky-Eared Pichu event, and its own game in Pokémon Ranger: Guardian Signs. I think Pichu wins this one, but I wouldn't say it's by a huge amount. Gen 2 - Pichu
Gen III also didn't really have a breakout Pokémon. I'd argue the contenders, though, are Metagross, Grovyle, Deoxys, Gardevoir, Blaziken, and the Lati twins, all for fairly small reasons. Metagross is pretty important in Gen III itself, but only in Gen III. It's Steven's ace, Beldum is a gift Pokémon in Emerald, it's Nascour's Shadow Pokémon in Colosseum, and is the first Pokémon you use in XD: Gales of Darkness. Grovyle is iconic to the Pokémon Mystery Dungeon series, being the main character of by far the most popular version (Explorers). Ash's Sceptile also stayed as a Grovyle for 95 episodes, which is a pretty long time for a mid-stage evolution, and a lot of its feature episodes were had during this period. Deoxys received its own movie and has its own location in every game except SwSh because it needs its mechanic of meteorites to evolve, and is pretty popular just because it's a cool design. Gardevoir is used by rival character Wally in its introductory game, and by later bosses like Nascour and Diantha. It's also a character in Pokken Tournament. Blaziken is perhaps the most iconic character for the Pokken Tournament series of games, and also features heavily in the anime as May's ace. The Lati twins got their own movie and their own feature in ORAS -- Pokémon Soar -- and also were used by the boss of Mt. Battle in the Orre games. Overall, though, while all of these Pokémon are fairly evenly matched, I think Grovyle edges this out -- circumstantially because a lot of people my age who grew up with the DS as their main console had Mystery Dungeon Explorers giving Grovyle a little more iconography in wider society (moreso than Pokken Tournament has managed), and because Mystery Dungeon Explorers is one of the best-regarded Pokémon spinoffs in the entire franchise. I can see this going other ways, though. Gen 3 - Grovyle
Gen IV is an easy one. Lucario is in Super Smash Bros., has its own movie, is a gift Pokémon in Sinnoh, received a mega, was Maylene's ace (and put up a tough fight), had an utterly iconic battle in the anime under Maylene, and is overall just extremely popular. Gen 4 - Lucario
I agree with the OP that Zoroark was the intended icon in Gen V, and I think they were probably more successful with it than any other Gen V Pokémon. The only contenders I can see are Volcarona and Hydreigon. Hydreigon was Ghetsis' ace, and Volcarona has a really cool design and its own room in the Desert Ruins. However, Zoroark got its own movie, was N's ace (who is the most iconic character from Gen V), and its own area in B2W2 -- Lostlorn Forest. Gen 5 - Zoroark
Gen VI is Greninja. It's in Super Smash Bros. and apparently got phenomenally popular in Japan. Plus, there's no competition because most of the designs in this gen weren't the best. Gen 6 - Greninja
Gen VII is Mimikyu, I agree with the above posts. The only competition is Silvally, which I think they're still trying to push to be more popular than it is. Mimikyu's totem battle is also incredible and the best part of Gen VII, which certainly helped its organic popularity. Gen 7 - Mimikyu
Gen VIII it's still pretty early to tell because nothing's been pushed too much yet. However, I'd argue the future contenders are Wooloo, Corviknight, Toxtricity, and Copperajah. Of these, Wooloo has the most prevalence in the main game, being the key character in the first plot point, first gym, and being Hop's secondary ace to the point of featuring in the first rival battle -- the first instance of the main rival having 2 Pokémon in the first battle (iirc). Corviknight is the main part of the taxi service and you see them dotted around the region, with an entire trainer class (Cabbie) being based on using the Pokémon. It's also just a really cool design that lends itself to some inherent popularity. Toxtricity is mentioned in this thread, but beyond it being awesome, a gift Pokémon, and featuring in the only cinematic of the credits alongside Rillaboom, I don't really see it being pushed that much. It's possible that it will get to the level of Zoroark perhaps, but that won't mean it's iconic, and currently I think it's less popular than Wooloo (which I'm predicting will feature heavily in the SwSh anime). Copperajah simply for being Chairman Rose's ace and featuring in a cutscene, alongside being an awesome design that could be pushed later on. For now, though, I'm saying Gen 8 - Wooloo
This is an interesting thread and thought experiment, thanks for creating it! If people disagree with my conclusions I'd be interested in hearing responses, as most of them are certainly subjective.