The first mechanical calculator was invented by Wilhelm Schickard. In 1632 he built a Calculation Clock. The details of this calculator were found in a correspondence between Schickard and Johannes Keppler. Several people have reconstructed this machine.
Blaise Pascal is regarded as the inventor of the mechanical calculator. He built his first calculator, a Pascaline, in 1643 to help his father (a tax-collector in Rouen, France). He produced about 50 pascalines in his lifetime.
The next machine was constructed by Sir Samuel Morland in 1660.
Gottfried Wilhelm Leibniz made a "steppen drum"-calculator. Only one of his calculators survived.
The first commercial succesfull calculator is the Arithmometer invented by Thomas Xavier de Colmar in 1820.(based on the Leibniz-wheel).
At the end of the 19th century many inventors followed: Baldwin, Odhner, Bolle, Felt & Tarrant, Burroughs, Hahn, Monroe, etc.
See: History of Calculators (Wikipedia)