I guess I will start based on my in-game experiences for most since I recently dabbled into competitive.
- SoulSilver opened my eyes to Ampharos, which I thought was nothing outside of looking adorable. While my scale sometimes slid back to dislike, it wasn't until it evolved to its last stage that it become fixed on my "great" scale. Typhlosion, however, went the exact opposite direction since it was dead weight to me half the time, to the point I swapped it out for Houndoom in the Kanto half of the playthrough.
- Black 2 and White 2 gave me two. The latter caused me to adore the hell out of the Magnemite line, which I never got to a Magnezone before, which I regretted boxing because I had a massive fighting weakness at the time. White 2 showed me the magic of Skill Link Cinccino when I scored one with Jolly and 31 atk and 25-26 spe. The thing was so god damn amazing I switched it to B2, re-did the EVs, and went on to get me my first win in the Champions PWT.
- My Y Nuzlocke caused me to change my opinions on Chesnaught and Talonflame. The latter was amazing and its U-Turns in conjuction with Lucario made dealing with Sturdy mons tolerable and Chesnaught was a massive tank even with Super Effective special attacks that kicked colossal amounts of ass. It also helped I finished my X run with a low opinion on Greninja. Furthermore, Talonflame made me want to try out Gale Wings one and it has served me very, very well in Wi-Fi.