Kanto
Regular: Alakazam
Abra was always one of my childhood favorites. When I grew older and learned that the fully evolved form was pretty much always the best, I grew to like Alakazam. This was during Gen 3. I really like it's high Sp.att and Speed, it is really powerful. It also has a great design, it has even got a moustache which is awesome.
Starter: Venusaur
All three Kanto starters have been my favorites at various points, but Venusaur has been my current favorite since Gen 3. I like its concept, it manages to combine animal and plant really well. I have had great success with it when I have used it in the games too.
Legendary/Mythical: Moltres
Like the previous two, this one became my favorite during Gen 3. Now that I look back at it, I guess it is a bit weird that I started liking all of my current favorites from Kanto during Gen 3, but that's how it is. I like Moltres, it is a cool phoenix-bird.
Honorable mentions:
Regular: Pidgeotto, Raichu, Primeape, Slowbro, Farfetch'd, Dodrio, Gengar, Krabby, Hitmonlee, Starmie, Snorlax, Dragonite, Vaporeon, Jolteon
Starter: Blastoise, Charmeleon
Legendary/Mythical: Zapdos, Mewtwo
Johto
Regular: Ledian
While it isn't very good in battle (I know because I have actually used it), I have always loved its design. I also have a memory from when I played Silver as a kid and spent a whole day training a Ledyba to evolve into Ledian, which is another reason.
Starter: Typhlosion
I have always had great success with the Cyndaquil line when I used it in the Johto games. I like their design too, especially how they can make their flames appear without having them being visible at all times. Feraligatr was my favorite as a kid but it didn't work that well for me when I used it in SoulSilver, so it is not my favorite anymore.
Legendary/Mythical: Suicune
Such an elegant Pokémon, it has an amazing design. I have used it to great success in many teams and it is also the mascot of Crystal, which is my favorite Johto game.
Honorable mentions:
Regular: Lanturn, Ampharos, Bellossom, Azumarill, Politoed, Espeon, Misdreavus, Scizor, Sneasel, Corsola, Houndoom, Kingdra, Mantine, Donphan, Porygon2, Smeargle, Hitmontop, Tyranitar
Starter: Feraligatr
Legendary/Mythical: Raikou, Lugia, Ho-Oh
Hoenn
Regular: Manectric
Choosing a favorite from Hoenn isn't the easiest since I think there are many great ones but few that stand out above the rest. But in the end, I'm going with Manectric. It has always been one of my favorites. I used for the first time I used it in Ruby and then I have used it in several other games too.
Starter: Swampert
I have always liked it ever since I first used it in Ruby. The Mudkip line has always worked well for me on my in-game teams in R/S/E and Omega Ruby, and I have had success with it in other games too.
Legendary/Mythical: Latias
One of the cutest Pokémon ever, it has always been my favorite Hoenn legend ever since I first saw it. I remember that I thought it could be obtained in Ruby but that required an Eon Ticket which I never got... fortunately, it could be caught in Sapphire and Emerald instead.
Honorable mentions:
Regular: Ludicolo, Swellow, Pelipper, Breloom, Slaking, Ninjask, Exploud, Skitty, Mawile, Aggron, Medicham, Camerupt, Altaria, Zangoose, Claydol, Cradily, Milotic, Tropius, Absol, Walrein, Huntail, Gorebyss, Salamence, Metagross
Starter: Blaziken, Sceptile
Legendary/Mythical: Latios, Regirock, Regice, Registeel, Groudon, Kyogre, Rayquaza
Sinnoh
Regular: Garchomp
The land shark. Garchomp has worked well for me on so many different teams, I like how it is strong, fast and has a great type combination. And I really dig its design too.
Starter: Infernape
Another fast and strong Pokémon. I used it for the first time in Pearl and it worked so well there, it has remained my favorite Sinnoh starter since then. It used to be one of my top favorite starters, but nowadays it faces fierce competition from other starters from the newer generations so I'm not sure about that anymore.
Legendary/Mythical: Shaymin.
A cute hedgehog with flowers, it creates flower fields, symbolizes gratitude and has an awesome alternate form. I love everything about it.
Honorable mentions:
Regular: Staraptor, Luxray, Roserade, Gastrodon, Ambipom, Drifblim, Lopunny, Mismagius, Honchkrow, Glameow, Happiny, Spiritomb, Lucario, Hippowdon, Mantyke, Weavile, Magnezone, Magmortar, Togekiss, Yanmega, Leafeon, Glaceon, Gliscor, Mamoswine, Porygon-Z, Gallade, Froslass, Rotom
Starter: Empoleon, Torterra
Legendary/Mythical: Palkia, Giratina, Mesprit, Cresselia, Manaphy
Unova
Regular: Haxorus
It has been my favorite ever since I first used it in Black. An awesome Pokémon overall with a great design, it is strong and powerful, it even has "Hax" in its name, what's not to love? I have used it on several teams over the years.
Starter: Serperior
A grass snake is a really cool idea, and it worked very well. I used it for the first time on Black too where it worked surprisingly well.
Legendary/Mythical: Reshiram
The mascot of Black which my first Unova game, and a really cool Pokémon. I like how it is strong and powerful with an amazing STAB combination, it has an epic design and it represents truth, which is awesome. That said, Keldeo is an extremely close second in this category.
Honorable mentions:
Regular: Stoutland, Simipour, Musharna, Unfezant, Zebstrika, Gigalith, Swoobat, Excadrill, Audino, Conkeldurr, Sawk, Seismitoad, Leavanny, Scolipede, Whimsicott, Lilligant, Krookodile, Darmanitan, Crustle, Scrafty, Sigilyph, Carracosta, Archeops, Zoroark, Cinccino, Gothitelle, Reuniclus, Swanna, Vanilluxe, Emolga, Sawsbuck, Escavalier, Amoonguss, Jellicent, Galvantula, Ferrothorn, Klinklang, Eelektross, Chandelure, Beartic, Cryogonal, Accelgor, Stunfisk, Mienshao, Druddigon, Golurk, Bisharp, Bouffalant, Braviary, Mandibuzz, Heatmor, Durant, Hydreigon, Volcarona
Starter: Emboar, Samurott
Legendary/Mythical: Keldeo, Cobalion, Terrakion, Virizion, Tornadus, Thundurus, Landorus, Zekrom, Kyurem, Victini, Meloetta, Genesect... wait, that's all of them!
Kalos
Regular: Sylveon
My favorite Eeveelution. A cute Fairy-type, that's all I need. I used it for the first time on X and I liked it a lot there, it is one of the things that made me fall in love with Fairy-types. I have used it on many other different teams too and it has pretty much always worked well for me.
Starter: Greninja
A strong and fast ninja-frog which is really cool. Like with Sylveon, I used it when I played through X. I have also used it on many different teams and it has pretty much always worked. I have never cared much for Ash-Greninja though.
Legendary/Mythical: Xerneas
The mascot of X, my first Kalos game. It is a Fairy-type, has a really cool design and it represents life, which I like.
Honorable mentions:
Regular: Diggersby, Talonflame, Pangoro, Meowstic, Doublade, Aegislash, Aromatisse, Slurpuff, Barbaracle, Dragalge, Clawitzer, Heliolisk, Tyrantrum, Aurorus, Hawlucha, Klefki, Trevenant, Gourgeist, Noivern
Starter: Delphox, Chesnaught
Legendary/Mythical: Yveltal, Zygarde, Diancie
Alola
Regular: Lycanroc
I love wolves, Lycanroc quickly became one of my favorites after I had used it in Sun. Midday form is my favorite, followed by Dusk, while Midnight is my least favorite (though it is also the only one I have never used).
Starter: Primarina
An elegant Fairy-type which is also really strong. It became my favorite after I first used the Popplio line in Moon.
Legendary/Mythical: Magearna
This is a weird case. I never cared for it when it was first revealed, but I fell in love with it after seeing it in the actual game. A Fairy-type robot maid, that's something I really needed in my life without knowing about it until I saw Magearna in the games.
Ultra Beast: Celesteela
The lazy bamboo-rocket princess from the Sanctuary Fortress. That's just awesome, and my favorite of the Ultra Beasts. It is also another thing I didn't know I needed in my life.
Honorable mentions:
Regular: Toucannon, Vikavolt, Oricorio, Ribombee, Wishiwashi, Mudsdale, Salazzle, Bewear, Tsareena, Comfey, Oranguru, Passimian, Palossand, Minior, Togedemaru, Mimikyu, Drampa, Kommo-o
Starter: Incineroar, Decidueye
Legendary/Mythical: Tapu Koko/Lele/Fini, Solgaleo, Lunala, Necrozma, Zeraora
Ultra Beast: Nihilego, Pheromosa, Kartana, Stakataka, Blacephalon, Naganadel
Galar
Regular: Copperajah
I have a hard time picking a favorite from Galar. These Pokémon are all so new, so I'm not really sure about my true favorite. But for now, I'm going with Copperajah. I like elephants and this one is really cool. I used a Copperajah as one of the 15 members of my team in Sword and it worked very well there, so I'm going with it.
Starter: Cinderace
This is the only Galar starter I have actually used, so that's why I'm going with it. Scorbunny was the one I picked in Sword since I liked it the best from the base forms, and I really like Cinderace too. It is strong and fast with a great signature move, it also has a great design and concept (and I have next to zero interest in football, so that says a lot).
Legendary/Mythical: Zacian
I mentioned that I love wolves. Well, how about a ridiculously strong epic blue wolf with a sword? That made this an easy decision. I recently got to use it on three different Battle Tower teams and it worked extremely well there. Everything about Zacian is awesome.
Honorable mentions:
Regular: Thievul, Eldegoss, Wooloo, Drednaw, Boltund, Applin, Arrokuda, Barraskewda, Toxtricity, Polteageist, Hatterene, Sirfetch'd, Runerigus, Alcremie, Frosmoth, Indedee, Morpeko, Dragapult
Starter: Inteleon
Legendary/Mythical: Zamazenta, Eternatus (they are both great, but I prefer Zacian)
Charizard: Was my first Starter, funny enough Blue version was my first Pokemon game. However, while I knew the little blue turtle would evolve to have cannons on its back (which is why my brother picked it), my focus was on the lizard with the flaming tail that'll evolve into a winged dragon with a flaming tail.
Heracross: Was a bit of a tough pick but I always had a small interest with Heracross. I think it was probably thanks to the anime, especially its battle with Scizor and tossing Scizor with its horn (which I thought was it using Megahorn but according to Bulbapedia it was Horn Attack). Plus Bug/Fighting is a pretty neat combination and came with a signature move in Megahorn which was a powerful Bug-type move (something notable back then as one reason Psychic-types were so strong was because there was no strong Bug-type moves).
Absol: Similar with Heracross, another tough choice but had a small interest with Absol. It just looks cool, a predator that attacks via the scythe attached to its head or its blade tail. It also had nice color balance, while most other Pokemon were brightly colored, Absol has pure white fur which gave way in spots for pitch black skin or sharp blades/claws.
Luxray: Tough choice, small interest with Luxray (sensing a pattern?). Actually I was considering Lucario as I do like it too... but when looking through all the Gen IV options once I saw Luxray I felt more drawn to it then Lucario. It's an electric lion that has x-ray vision, awesome! It's ruffled hair also made it look wild, like its ready to pounce. If you can't tell by now I more like the cool and fiercer looking Pokemon.
Braviary: When they made a region based on the US one Pokemon I wanted was on based on the bald eagle, and I got it! And it looks great, a big bird of prey with Native American war bonnet. How more American can you get?
Noivern: I like Noivern for the few subversions it does (and because it looks cool). First off it's definitely a bat Pokemon but it's also a dragon which is an interesting combination (we've had lizards, dinosaurs, and birds being dragons but I haven't heard of a bat dragon). Also it's first Type is Flying with its second Type being Dragon, a small novelty that doesn't really mean much in the long run but I like it cause it does explain why it looks more bat-like with dragon inspirations then the other way around.
Mimikyu: I think I remember not liking Mimikyu the first time I saw it. "Really, GF? It looks like a two year old drew this Pokemon". Then I learned what it was about and my heart sank. However I think what finally really sold Mimikyu to me was Pokemon Company making a song just for it where it sings about it not being Pikachu but wants to be friends because it's lonely (then in the anime Jessie caught one which had a massive hatred toward Pikachu and it was by far one of their most competent fighters even if it let its hatred get the better of it).
Toxtricity: I didn't really know what to think of it when I first saw it from the leak. I did think its Typing was pretty cool but wasn't sure if I would use one. Then I got a Toxel via the Daycare and, well, I guess I would use it afterall. Yamper wasn't really impressing me and Poison was a useful Type to have if you want to wear down the opponent so fit into my team. And I took it all the way to the League, it's still on my team now as its surprisingly versatile and hits hard with its Overdrive. I could take or leave the gimmick, it's cool at first but when I learned my Low Key Toxtricity didn't learn Venoshock so had to grind in the Wild Area until I got the Sludge Bomb TR irked me a bit. But hey, it did mean I taught my Toxtricity a more powerful move so worked out in the long run. Plus you gotta love it's animations where it's playing air guitar :). ROCK OUT!
