I recall a fight in the Battle Tower where the last Pokémon was a Ghost-type that KO'd itself with Curse.
As for battles with friends...
Once I was doing a battle against a friend who had a team of mostly legendaries, including a hacked Darkrai (this was pre-movie event). His last Pokémon was said Darkrai, and I had out at the moment my Lucario, which had just barely managed to defeat his Palkia. Darkrai is faster and moves first, but its attack (I forget which) leaves Lucario with just 1 HP, and Lucario one-shots it with Aura Sphere.
Then there was another time I battle a different friend in the Union Room and completely threw her off by using Rotom, which she had no idea what it was, and more than once forced a draw with Electrode blowing itself up...
Then I insisted on a full-out battle since I was bored of using low-levels, but since I was way ahead level-wise (she hadn't beaten the Elite Four yet) I decided to play nice and use mostly Pokémon of the same level as hers that I didn't use. It was an okay match, but since hers were actually trained, they took out most of my unused guys. My last Pokémon was... my Lucario, which slaughtered the rest of her team as I laughed maniacally.
Oh, and I can't believe I forgot- I caught Mesprit with a single Quick Ball the first time I saw it. I thought "eh, what the heck, worth a try"... and it worked!