For me most Gym leader battles aren't terribly memorable, but these make this list for one specific reason.
I started my very first Pokemon journey (and nearly all subsequent playthroughs of Red/FireRed) with Charmander, the Fire type starter Pokemon. When you arrive in Pewter City you can't progress until you've faced the gym leader Brock. Brock happens to specialize in Rock types, which is an absolute joke if you picked Bulbasaur or Squirtle to start. Needless to say I've had to either grind or get really lucky many times when facing this guy.
Then you arrive in Cerulean City, where the gym leader Misty uses WATER types. That's right, Water. This one's even harder than Brock, and unless you've raised a Grass or Electric type, you're in for a rough fight.
Overcoming both of these obstacles, especially that early in the game, really set the tone for all my Pokemon battles to come. I learned that I couldn't just bulldoze through every challenge... I had to adapt, to strategize. To this day I always take my type matchups into consideration, and I feel I'm prepared to take on just about anything.
The only other Gym leader that's given me that much trouble is Whitney and her Miltank... but that thing has got to be a demon.