Kanto: In R/B, Misty. Her Starmie was brutal. In FR/LG, Sabrina. Alakazam outsped and killed me constantly. Also, Calm Mind.
Johto: Clair. It took me a good 20 times to beat her back in Silver. I'm dead serious. That freaking Kingdra. >.< Also didn't help that Typhlosion was pretty much my only leveled up Pokemon at that point. I know, I was a stupid kid. I even had trouble with her in HG/SS with a well-trained Raikou.
Hoenn: A tie between Norman and Tate and Liza. Norman's Slaking would always give me trouble and it took me forever to KO it. I had an overleveled Hariyama on my team and it was still OHKO'ed by that Slaking! I needed to have my Pelipper use Protect when it was attacking and when it was loafing around I used Surf which barely did anything so it took me a half hour to beat it.
And Tate and Liza? Holy crap they were horrifying in all three games, especially Emerald. No matter how well balanced my team was, they would always have one move that was super effective on each one of my Pokemon.
Sinnoh: At this point I was getting better at level grinding, so I had no problems in D/P, but Fantina was a pain in Platinum. I needed to go back and catch a Buizel and evolve it before I could even touch her Mismagius.
Unova: No problems, but Elesa's Volt Switching was just plain annoying.
Kalos: By far the easiest Gym Leaders ever, but one does not simply OHKO Valerie's Sylveon.