Neil Haverstick is a well known guitarist whose compositions include explorations of exotic microtonal realms. He uses a large variety of microtonal guitars including 19, 31 and 34 tone equal temperaments and fretless guitars tuned to the harmonic series. Here is a collection of his 34 tone guitars. Notice how close the frets are to each other.
Dante Rosati uses a just intonation guitar, a harmonic guitar and a very unusual prime guitar that uses ratios of purely tuned prime numbers up to 199. You can also hear some of his music at his Zebox page.
Doctor Oakroot plays a rough edged type of blues on homemade guitar-like instruments. Some of the instruments are based on Pythagorean tuning and one uses 17 tone equal temperament. Here's a video of him playing a homemade guitar.
Doctor Oakroot-Snake in the Grass
If you are interested in making homemade instruments, you might like to read his article on how to make a diddley bow (a cool, but simple, instrument with microtonal capabilities).