Are there aircraft that fly without fuel or electricity?
Yes, there are so many sources of energy you can use.

In the simplest form we have Buoyancy, Human power, Fly wheel, Rubber band. 

More complicated mechanisms include compressed air, steam, hydrogen peroxide, which you can either use directly as a rocket/jet, or drive a piston engine or turbine to further drive a fan or a prop.....

Or, if you prefer, you can never go wrong with nukes

(Although one could argue nuclear and peroxide(and other mono-propellants) are fuels)

Here I'll just present my favorite out of all the possibilities.

Picture credit: TIHOOD