A friend of mine had an acoustic guitar with a pickup under the saddle. He attached another transducer directly to the back of the soundboard. He took the output from the saddle pickup, ran it through his effects pedals, and back to the soundboard transducer. The result was an acoustic guitar with distortion, delay, chorus, etc. The sound was produced completely by the soundboard of the guitar vibrating, just like any other acoustic guitar, and at the same volume -- no amp, no external speakers. Acoustic or electric?

I'm amused by all the comments about electric guitars being bad because they are played too loud. This is the fault of insensitive musicians, not the type of instrument they are using. Amps have volume knobs, and electric guitars can be played substantially more quietly than acoustics and still sound good. There are also lots of insensitive acoustic players who drown out other instruments.