As of 2012, there are 118 known elements
Elements consist of particles called atoms that consist of protons, electrons and optionally neutrons. Protons and neutrons are in the core of the atom, while electrons reside on different energy levels in a cloud around the core.
The atomic number of the element is determined by the number of protons in the core. The lightest, simplest element in the universe is hydrogen-1, which consists of one proton and one electron. There are also isotopes (different types) of hydrogen that have one or two neutrons in the core.
Since the number of protons defines the element, we can create a different element by adding more protons to the core. To make the new element an atom, we need to add a corresponding number of electrons, since protons are positively and electrons are negatively charged and an atom is always neutrally charged.
The more protons and neutrons you add to a core, the bigger it gets. When the core gets bigger, it also gets more unstable. This puts limits to what kind of elements occur in nature and also causes some elements to be radioactive.
The speed of light limits the number of different elements that occur as neutral atoms (where there are as many electrons as there are protons) to about 176.
The number of different elements that are proven to exist is 118, with the largest atom being number 118 (temporary name ununoctium), since element number 119 is yet to be found.