At the most fundamental level, all the forces in the universe come from only four forces (as currently understood):
These forces are known as the fundamental forces. Some theories link the electromagnetic and weak forces and call this the electroweak force. Other theories attempt to unify the strong force as well and then have only two forces.
These forces combine to form the everyday forces in day to day life:
The gravitational force acts between all objects that have mass. It always attracts objects together, and although it is the weakest fundamental force, it has infinite range (it does get weaker with distance). The force of gravity pulls objects towards Earth, causing things to fall. It also keeps planets and moons in orbit. The force of gravity from our moon acting on the oceans causes tides. This is also the dominant force that gives hydropower its energy.
Electromagnetic forces act between charged particles. Opposite charges attract, while objects with the same charge will repel each other. Many "everyday forces" are truly electromagnetic forces on an atomic level added up to a large scale. For example, pushing a box exerts a force on it because the negatively charged electrons found in atoms in the hand pushing repel the negatively charged electrons in the atoms of the box. Electric fields and magnetic fields involve these interactions. Electromagnetism is responsible for many very important interactions, such as chemical bonding.
The weak nuclear force converts protons to neutrons in fusion, or neutrons to protons in other nuclear reactions. It has very short range and is relatively weak. Modern physics has unified the electromagnetic and weak forces into the electroweak force. People continue to try to unify all of the forces in a grand unified theory.
On a small scale, the strong force is responsible for binding together the particles (quarks) that make up a proton or neutron. On a larger (but still very small) scale, the residual strong force is responsible for holding the nuclei of atoms together, despite nuclei containing many protons, which would otherwise repel strongly due to the electromagnetic force. This force is extremely powerful over short distances and is responsible for the massive energy stored in nuclear fuel and released in nuclear power.
For more information on the fundamental forces, please see hyperphysics.