Okay, by “random NPC” I am understanding you to mean excluding Professors, rivals, Gym Leaders, villain bosses, Champions, Elite Four members, and other similar recurring character archetypes? Um… I’ve never really given it a great deal of thought but I guess there are a few I have fond memories of…
The Super Nerd from Mount Moon. He had his priorities straight – live in the dark, hoarding the calcified remains of extinct animals and responding with violence to anyone who tries to take them. Or the Aroma Lady outside Mauville City in Ruby and Sapphire who can inexplicably walk up ledges. Or the old guy with the Weedle in Viridian City who tries to teach you how to catch Pokémon but fails miserably! Man, good times… And who could forget Youngster Joey with his top percentage Rattata?
Also, I don’t know whether he counts as “random” but I have a certain fondness for Zinzolin in Black and White 2, purely because his motivation in those games is totally at right angles to what everyone else in the plot is concerned with, but still actually kind of interesting (he wants to separate Pokémon from people just to see what will happen, in a kind of twisted social experiment).
Pokémaniacal 