So many! Getting attached to my Pokémon is one of the things I really like when playing the games. I never reset my game, I'm too sentimental.
Only from Ruby, there is my first starter Blaziken and my constant team members Swellow, Linoone and Lanturn. My Mightyena that knows Dig and fainted from poison after evolving before I could get to the Pokémon centre. My jolly Castform. My Slaking that knows Focus Punch. My Abra that I caught with a Master Ball because I was little and didn't know better. My Delcatty that I raised to level fifty-something before realising she evolves by Moon Stone.
I also get attached to Legendaries, especially in gens 3 and 4. They were hard to catch or came from special sources and were really memorable - the Lake Guardians, Cresselia, the female Heatran from Mt Stark, the male Eruption Heatran, Shaymin, Manaphy and Deoxys from Ranger: Guardian Signs, the shiny Legendary beasts from the Zoroark movie giveaway...
Ooh, and foreign Pokémon from the GTS back in gen 4. Our Piplup was Japanese and our Turtwig was Mexican - we like to joke that he'd watch Mexican soap operas when he felt homesick, haha.
That's off the top of my head, haven't scratched the newer generations (my female Incineroar from Moon, or my Galar mons...).