I've had some close games, but the most rewarding was always the bot lane matches that were so well fought and close. The type where you only win by a twitch reaction or nailing that skill shot just right as you both have less than 100 HP.
Remember one that I was Ahri vs a Wukong. We were so close, back and forth, he'd always sneak away with just slivers of health due to the decoy. Got a Sweeper, then it changed in my favor, holding bot from then on, and just doing the solid play that let the rest of the team up top bring it in for the win.
I also remember playing vs rickless before I was a rioter! He was Ez and I think I was Lux or something. Again super close, but he just barely got an edge on that one and that was that