If you want to get technical, it was in the 1940s. it was the size of a small house. see http://en.wikipedia.org/wiki/ENIAC if you are thinking computers roughly the size you see them today, the answer could be argued between the 70s 80s and 90s. in the 70s you had the Xerox Alto, in the 80s you have the Macintosh and the IBM PS/2, 90s is when you start seeing more modern things though.
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If we confine ourselves to electrical apparatus, probably Konrad Zuse in Germany, around 1934-1941. Charles Babbage (England) is ususally credited with inventing the first mechanical computer, around 1850-1870
http://en.wikipedia.org/wiki/Konrad_Zuse http://en.wikipedia.org/wiki/Babbage
The first consumer computer appeared in 1974/75.
But the first "freely programmable" computer appeared in 1936.