Water and steam just too goddamn convenient. Super high latent heat so it can move a ton of energy with a quick phase change, works at reasonable pressures and temperatures, stays liquid all the time when you want it to so pumps work, and it's so readily available as to be damn near free. Super cool!
Solar photovoltaic is the only one i can think of that isn't just a fancy way to make steam
EDIT
ok let's clarify to say a method that isn't related to movement of a fluid that spins a turbine. So not windmills (air is a fluid), not hydro, not geothermal, etc.
Some types of fusion can bypass steam generation and use what's creatively called Direct Energy Conversion. If the fusion products are charged particles they can be passed through a magnetic field to separate them based on charge and collected onto plates. When you look at the electric potential between the plates you've effectively created a voltage, no steam necessary.
It's also theoretically possible to do the same with some types of fission products too.
I like piezoelectrics and kinetic generators. The only two methods of generating electricity I know of that don't involve steam other than solar panels.
At least, I think they're different... Is a standard copper wire+magnet generator pizeoelectric? Or is it simply the operation is similar in that you generate electricity from moving things together? Like the difference between tiny little things in your shirt that generate electricity as you move around vs those flash lights you shake to charge.