There are nine main types of energy, but these can all be classified as kinetic or potential energy.
The main types of energy can be classed as potential - if it is stored, or kinetic - if it is active (this is because energy types, like heat, are caused by the atoms possessing kinetic energy - don't worry too much about that if it makes no sense).
Here are the nine types of energy and an example for each:
Kinetic - the energy possessed by all moving things example: a car that is driving along a road has kinetic energy, which is what causes it to continue moving
Heat - example: when you burn oil in a heater, you are transferring chemical energy in the oil to heat energy
Sound - example: whenever you hear something, that is due to sound energy, or more specifically, kinetic energy causing particles to vibrate which are then interpreted by your brain as sound. So a CD player transfers electrical energy into sound energy when it plays you a song
Electrical energy - this is the energy carried by charged particles (e.g. electrons). We use electricity as a way of powering pretty much all devices example: electrical energy is carried along power lines to houses where it is then transferred to other types of energy by a device
Nuclear - this energy is as a result of change in the nuclei of atoms example: nuclear fission (an unstable atom splitting) and fusion (multiple small atoms joining) are both examples of nuclear energy, and are used to produce electricity in power stations.
Elastic potential - example: when you stretch a rubber band, the kinetic energy you use stretching it is stored as elastic potential until the force (your stretching) is released (then it turns back into kinetic).
Chemical - example: humans consume food that contains carbohydrate, or glucose. The food we eat contains stored chemical energy, because they will release energy when combusted
Gravitational potential - When an object is raised above the ground, it is said to have gravitational potential as it has the potential to accelerate towards the earth (due to gravity) once no longer supported. example: a book is knocked off a high shelf and accelerates, or travels, towards the floor - it's gravitational potential has been transferred to kinetic energy.
I hope these are enough, or the right type of, examples. Let me know if you need any more information, or if I have got the wrong end of the stick completely! Hope this helps:)