Kinetic: ANYTHING that moves. Sometimes you split it up into normal kinetic and rotational kinetic (where rotation just means it's spinning)
A moving car
A moving bird
Planet Earth (relative to the Sun...)
all have kinetic energy.
Potential is just where, if you stopped 'holding' the object somehow it would move.
Gravitational potential - ANYTHING that's not at the centre of mass of the Earth has gravitational potential energy from Earth.
You (if you removed the ground you're standing on, you'd fall through it to the centre of the Earth!)
Anything that's held together or pushed apart by an electric or magnetic force. This is what chemical potential energy is: the atoms are held together by electrical forces and they can be made to share electrons which sticks them together.
This is what elastic potential is too: the atoms share electrons and when you pull a rubber band you make the distance between the electrons (negative) and protons (positive) in each atom get bigger. The negative and positives are opposite, so they attract and try to pull each other back together. If you stop stretching the elastic, then it springs back together (like gravity. If you stop holding it, the potential energy is released and converted to kinetic!)
So electromagnetic potential (which includes elastic, chemical etc) examples are:
A stretched rubber band, jump rope or trampoline
A chemical bomb like dynamite
A charged battery
A charged capacitor