I don't know if this happens to everybody else, but my favourite mons are a mixture of designs that I like and Pokémon that have proven useful to me. Maybe it's difficult to explain, but when I feel a Pokémon is somewhat strong or useful to me, its design grows on me. Some of the Pokémon in this list may be susceptible to change, but the ones that are there to stay are Ho-Oh, Scizor, Gyarados and Porygon2, my 4 favourite mons in that order.
I've always liked Scizor. Back in GSC days, the Steel type felt so cool. I didn't know shit about competitive nor in-game inner mechanics, it just was a new typing capable of resisting a lot of shit. Steelix is also a favourite mon of mine, and I was so mad everytime I played GSC because I don't like nicknames on mons, but the earliest way of obtaining an Onix was by trading it with the guy on Ciudad Malva (don't remember how's it called on the english version rn lel), no way I'd travel through the Dark Cave without Flash, and his Onix was named Rocky or some shit like that. Then, I forgot about it in Gen III. I loved its design but the lack of a competent in-game movepool made me choose other mons, and then in Gen IV we all know what happened.
Gyarados is a must. Intimidate and Moxie after Gen V, incredible typing, access to DD, differences between male and female, always a threat, especially in Gen IV, I ran bulky DD gyara with subs/taunt a lot. Zapdos is another 'mon i've ran a fkn lot. Timid, modest, as offensive pivot, bulky with leftys, after it gained static it just became x1000 times better that it already was, random access to heat wave... I don't use Clefairy (trust me o.o), I like its design. Ever since it was Normal type, I just really liked the mon design and still do. This time it has nothing to do with its competitive capabilities. The same can be said about Metagross. It was my main in-game mon in Sapphire and the first mon I hard grinded to level 100 in the Elite 4 (with no lucky egg ;_;), and it was really good in DPPl, but again, purely because of its design. Heatran is a mon i've spammed in 2 millions teams. I like the design and its one of the best Pokémon i've seen in my life in this franchise. Torment, Subs, Lava Plume, Eruption, Magma Storm, Fire Flast, Flash Fire, spa high af, defensive stats high af, specially combined with arguably TOP 3 defensive type combinations in the game, SR, Roar, Toxic, Earth Power, Flash Cannon, Scarf, Specs, Leftys, Explosion, random Z Grass Attack thanks to Solar Beam... This mon is the very definition of versatility. Venusaur is my favourite starter and again, I like how it has gained power over the years until the point it could easily sweep an entire team in sun. I really like mons that are either capable of sweeping opposing teams with ease or, if running a different set, became an entirely different mon, a hard wall, because you can run them however you want. Skarmory is a fkn beast and its design is so cool, Crobat favourite poison type, no doubts, I was doubting between Para and Volca, but I choose Para. He was my first shiny in leaf green, also, I have always thought this mon could be so good if they changed some things about it. Its ability is cool and a Pokémon that has Spore is always useful, he also has some good support moves like Leech Seed and Stun Spore. His attack is not that bad (it learns swords dance, and altho SD is not usually that useful on slow mons, this can be bypassed with Spore), but it fell to mediocre after the power creeping...