Here's what just happened to me: The sparkplug cap, which screws directly into the spark plug wire, had come unscrewed a bit, and was keeping the engine from running.
It happened right after I changed the plug. I changed the plug back to the old one, and it started working, but it was only because in doing so, I'd jiggled the cap and wire enough to make contact again.
I snugged the wire to the cap to fix it, i.e. I turned the cap clockwise on the wire until it was lightly snug. (Until the guys here on the forum pointed that out to me, I'd had no idea that could even go wrong.)