Steelix, because it is a huge snake made out of rock/metal boulders, has a lantarn jaw of justice and looks perpetually pissed off. What is not to like? Part of the appeal, perhaps, was also its unavailability. Steelix could only be obtained through trading and none of my friends played pokémon. So for most of my youth I could only admire Steelix from a distance...
It still hurts.
On the other end of the spectrum:
Lilligant, the dancing queen, the belle of the ball. One of the first pokémon I caught in BW was a Petilil and I didn't have high hopes for her, but I needed a Grass type, so whatever. She grew on me and when she evolved into a Lilligant she turned out to be a pretty good pokémon! A one-trick-pony, but a good one nonetheless.
Now, if Lilligant is available in a game, she will likely be on my team in my first playthrough.
Honorable mentions:
Scyther, the OG badass motherfucker. Rare as hell, too, in Red at least. One look at its sprite and I was sold.
Umbreon. I like all eeveelutions, but Umbreon is the best. Such a sleek design. Simple but effective. A shame the developers decided to make Umbreon the eeveelution purely focusing on defense. As someone whose strategies boil down to "attack, attack, attack", poor Umbreon tends to get sidelined.
On the other hand, I have walked over 100 km with Umbreon at my side in Pokémon Go. That has to count for something, right?
Mismagius, one of the better new evolutions to be introduced in D/P/Pl (together with Roserade). I like Misdreavus a lot as well, though, so I don't always evolve it.
Nidorino. I have been a fan of him since I saw him battling Gengar in the opening animation of Pokémon Red. Look at that grin; that determined look in his eyes. He is awesome and he knows it.