On a lowracer, believe it or not, a poncho works. Tuck the bottom front into your shorts and sit on the bottom rear. If you do it right, the exiting air will collapse the poncho at your shoulders. Your feet arms and legs WILL get wet, as will your head but your core will stay warm.
For me that's emergency-only. I normally don't ride if there's a significant chance of rain. Sometimes, though, I'm on a tour where it's unavoidable. For instance, I've only heard of ONE time where there wasn't rain on TOSRV. I avoid the rain by avoiding the ride.