Wow, while spending the time to read through the thread, far too many non-evolution pokemon popped up in my head that I like, so I think I'll list a few of them.
Pinsir- As soon as I saw its card, I loved the leaping pose it made, and when I used it in Blue version, its Guillotine worked more than the vast majority of pokemon I used one-hit-KO attacks with. Also, well just look at its mouth, it's so awesome!
Farfetch'd- It's one of the only pokemon with a weapon at its disposal (an edible one at that), and I always liked that Farfetch'd episode of the show from the first season.
Dunsparce- Pokemon's underdog. Back when I had an interest in using pokemon that were hard to find instead of using strong ones or easy to train ones, Dunsparce seemed to hold more power than commonly rumored. I also liked how in Crystal, it drilled its tail when it appeared.
Miltank- Miltank was always a plague when it was used against you in your 3rd gym match, making the only options aside from long training sessions being to get a Rock type or trade for the Machop in the Goldenrod Dept. Store. However, it didn't take long for the game to give you a chance to get your own Miltank, so you can cause everyone else the same insanity that Whitney caused you.
Aerodactyl- As soon as I got a GSC official guide book, I saw the true power of Aerodactyl. Its speed matched Electrode for highest in the game. Also, with decent attack and a supportive movepool at its disposal, I always made sure my Aerodactyls couldn't lose.
