Regular Trainers:
That duo on Route 47 with the Magmar and Electabuzz. I had Lapras (who was weak against electric attacks) and Flaaffy out, and they were paralyzed within minutes. Fortunately, Flaaffy managed to paralyze both Electabuzz and Magmar, too. Both of them hung on for a while, but I eventually had to pull Lapras out and switch in Quilava. She was quickly inflicted with paralysis as well, but she and Flaaffy hung in there and took down Electabuzz (I'm pretty sure Magmar was out of there by the time I made the switch).
The first Skier in Pryce's Gym. That Jynx froze my Ampharos solid twice in a row! What are the chances? The next time I faced her, I equipped Ampharos with an Aspear Berry, and guess what? The Jynx didn't even use Ice Punch…
Any trainer in the game with a Pikachu as their main Pokemon. Double Team, Thunder Wave… that pretty much sums it up. Not to mention their ability has a chance of paralyzing any Pokemon that uses a direct attack on them.
Gym Leaders:
Morty, Morty, and did I mention Morty? His Gengar's Shadow Ball pretty much wiped the floor with my Pokemon. The Pokemon with the best Special Defense on my team was Quilava (whose Special Defense is average at best… guess what that says about the rest of my team?), and she still lost a good 50-60% of her HP from one attack. She was also the fastest Pokemon on my team, and still unable to beat out that Gengar in speed. I think the only reason I managed to put that Gengar away was because of a critical hit with Flame Wheel.