If I push someone, what fundamental force do I create? According to Wikipedia, all forces can be decomposed to four fundamental forces: gravity, electromagnetism, strong interaction and weak interaction.
When I push someone, this generates a force. Which of the 4 forces is this composed of?
 A: When you push someone,
You are actually trying to compress intermolecular distance between the atoms of the body. Atoms contains charged particles (initially in equilibrium) and when disturbed by the force they show reluctance (opposing force) which is Electromagnetic in nature. 
Best example can be considered as the Normal force acting between two stationary bodies kept in contact.
A: Electromagnetic. The electrons in your hand do not want to be too close to the other person's electrons. So they repel.
A: 
If I push someone, what fundamental force do I create?

When a human pushes a object through physical contact, the nature of the force between the human and object is electromagnetic. Atoms consist of positively charged nuclei with negatively charged electrons in orbitals around the atoms. When two atoms are close enough, the electromagnetic force of repulsion between the electrons becomes significant, and the electron orbitals become deformed.
The strong, weak and gravitational forces are insignificantly small in this context.
A: Most answers are concerned with the force that transmits the push from the pusher into the pushee, but there's another way to understand the question: what force is behind the arm that pushes, i.e. where is the force generated and which elemental force is it due to? Ignoring a vertical push upwards, in a push you actually combine two forces: the gravitation of your body weight, and you feet's friction on the floor.
Basically, you lean forward, and then because your foot is on the floor and doesn't slide (i.e., friction) gravity exerts a torque (a twisting force) on your body which makes you fall forward.  Your hands push against the pushee, and the reaction force balances this torque, preventing you from falling forward.  You can convince yourself easily of the role of gravity by thinking what happens if you push something that won't move: if you push too hard your body starts to rotate about your feet with your center of gravity moving upward.  This work done is done against gravity.
All the static forces (friction on floor, the structure of your body, the force transfer in the point of contact) are electromagnetic in origin (+ Pauli principle, see John Doty's answer), but the force that actually gives you the ability to push is gravity.
A: The answers are all conventional, and all misleading. Electromagnetic forces in solid matter are essentially attractive: if you take a solid object and compress it, the electrostatic binding energy increases, so matter should simply collapse. What prevents this is Pauli forces, which are both repulsive and directional. These are due to the Pauli exclusion principle: compressing an electron cloud raises the energy of the electrons as they avoid each other in phase space.
This manifests itself as a real physical force. You can feel and measure it. It does not, however, show up as a "force" in the mathematics, so some claim it isn't a force.
This happens in classical mechanics, too. In the Hamiltonian formulation, constraint forces disappear from the equations of motion. Nobody, however, would claim that there's no force on the fulcrum of a lever because it fails to appear in the equation of motion. You can even put a force gauge on the fulcrum and measure it.
So, the way to understand solid matter is in terms of balance between the essentially structureless attraction of electrostatic force balanced against the structured Pauli repulsion.
So, when you push someone, you disturb this balance, and the result is a force between you and the other person.
A: When one body pushes another, this is just an example of momentum conservation. It is a classical principle which does not require quantum mechanical effects as suggested in some of the other answers and which holds for any type of interaction (a push which a moving particle exerts on a particle at rest in a 2-particle collision is the same whether the interaction force is a repulsive or an attractive force, it is only that the details of the orbits are different).
In the case of macroscopic bodies, the interaction forces on contact would essentially only be the electrostatic repulsion between the positive ions. The electrons are dynamically irrelevant due to their small mass. They just move around according to whatever the charge configuration of the ions is. From Newtons law $F=ma$ you can see that if you push an object with acceleration $a$, the force due to the electrons is negligible, simply because the mass of the electrons is a couple of thousand times smaller than that of the ions. So essentially all of the push-force is due to the ions.
The Pauli exclusion principle mentioned in some of the other answers would only potentially prevent that the skin of your hand merges with the object or person you are pushing. It is not responsible for the pushing effect as such.
