Mine was a battle against a maxed out Amnesia on a Slowbro...took an hour to win with a Nightshade & Mega Draining Gengar. Also the battle against your Rival's Alakazam...stupid recover... it took a little over a half hour to take down...would have won faster but my Jolteon fainted before I could launch a Pin Missle, but good ol' Gnegar helped out again with it's Hypnoises & Dream Eater combo...
My most annoying capture was a Gastly with a high special and defense, I captured a close 15 Gastly's before I found one I liked...another was when I tried to capture a Magmar, it took me 15-20 minutes just to find one...any way post your most annoying battle or the capture of an pokemon here.