Metal-air batteries/fuel cells. Made a mini aluminum air battery (you can easily DIY one with household items). It seems that most people consider metal-air batteries to be a dead-end, since they aren't green and are generally non-rechargeable, and air cathodes are tricky (sluggish, exotic materials, expensive catalysts). I dove into "alternative" battery and fuel cell research after looking into how to extend the range of my electric motorcycle. I love the electric drivetrain, especially on motorcycles, but lithium ion isn't up to the task as far as capacity for anything beyond an hour or two of high performance fun. If I could get a compact metal air battery or hydrogen fuel cell to output just 1kw for a hybrid drivetrain, range issues could be solved.
It's still more of an idea/crude experiment than a project right now. There are some neat videos of DIYers with similar projects though - small homemade metal air batteries and materials experimentation. Aluminum air seems to attract the most attention. There is also a lot of available research.