This happened to me on my Pearl version
I was just being bored one day, and decided "Well, since i haven't gone to Shaymin's alter(the grey rock) i'll do it now."
I decided to actually go through the Victory Road, but i had an Action Replay in, and turned on Run through walls....Heh.
I found Marlely, let her come with me, and i decided to "make a shortcut." I cut across some water, and got into a wild battle.
I saw TWO of my charater, and one of the wild Pokemon was um, a white block. Marleys Arcanine was a white block too. And Marley was ME. Yes, ME. She turned into my charater. I didn't know what the heck was going on, but i WANTED that white block!
"I must have #494!"
....Then i relized what the white block was. It attacked Marleys Pokemon with Struggle, and killed both of them, leaving my lv 100 Jolteon vs. a lv 50+(or so) Golbat...
I looked up the White block, and found out it was Missingno.
SO that concludes my random/weird encounter on Pearl