In Pokemon Ruby, I ran into a shiny Electrike, but at that time all my Pokemon were level 40 or above and it was level 13 or so, so I couldn't weaken it, wasted all my balls on it, and then knocked it out :/
BUT in Diamond, I was able to wrangle myself a Buizel
It's worth noting that, after my failed encounter with Electrike, I turned my game off and back on, put a weaker Pokemon in my team, and stood in that patch of grass looking back and forth trying to find it again for about 20 minutes. Derp.