It is difficult to identify any one device as the earliest computer, partly because the term "computer" has been subject to varying interpretations over time. Originally, the term "computer" referred to a person who performed numerical calculations (a human computer), often with the aid of a mechanical calculating device.
The history of the modern computer begins with two separate technologies - that of automated calculation and that of programmability.
Examples of early mechanical calculating devices included the abacus, the slide rule and arguably the astrolabe and the Antikythera mechanism (which dates from about 150-100 BC). Hero of Alexandria (c. 10–70 AD) built a mechanical theater which performed a play lasting 10 minutes and was operated by a complex system of ropes and drums that might be considered to be a means of deciding which parts of the mechanism performed which actions and when.
This is the essence of programmability.
The "castle clock", an astronomical clock invented by Al-Jazari in 1206, is considered to be the earliest programmable analog computer. It displayed the zodiac, the solar and lunar orbits, a crescent moon-shaped pointer travelling across a gateway causing automatic doors to open every hour, and five robotic musicians who play music when struck by levers operated by a camshaft attached to a water wheel. The length of day and night could be re-programmed every day in order to account for the changing lengths of day and night throughout the year.
The end of the Middle Ages saw a re-invigoration of European mathematics and engineering, and Wilhelm Schickard's 1623 device was the first of a number of mechanical calculators constructed by European engineers. However, none of those devices fit the modern definition of a computer because they could not be programmed.
In 1801, Joseph Marie Jacquard made an improvement to the textile loom that used a series of punched paper cards as a template to allow his loom to weave intricate patterns automatically. The resulting Jacquard loom was an important step in the development of computers because the use of punched cards to define woven patterns can be viewed as an early, albeit limited, form of programmability.
It was the fusion of automatic calculation with programmability that produced the first recognizable computers. In 1837, Charles Babbage was the first to conceptualize and design a fully programmable mechanical computer that he called "The Analytical Engine". Due to limited finances, and an inability to resist tinkering with the design, Babbage never actually built his Analytical Engine.
Large-scale automated data processing of punched cards was performed for the U.S. Census in 1890 by tabulating machines designed by Herman Hollerith and manufactured by the Computing Tabulating Recording Corporation, which later became IBM. By the end of the 19th century a number of technologies that would later prove useful in the realization of practical computers had begun to appear: the punched card, Boolean algebra, the vacuum tube (thermionic valve) and the teleprinter.
During the first half of the 20th century, many scientific computing needs were met by increasingly sophisticated analog computers, which used a direct mechanical or electrical model of the problem as a basis for computation. However, these were not programmable and generally lacked the versatility and accuracy of modern digital computers.