Nuclear power plants have been build in several sizes. The nuclear reactor to generate electricity was EBR-1, the Experimental Breeder Reactor number 1 in Idaho. On December 20th 1952 it generated enough electricity to power four light bulbs!
On June 27 1954 the Obninisk Nuclear Power Station in the USSR became the first nuclear reactor to provide electricity to an electricity grid. It was a 5MW (electric) reactor.
In general the larger a reactor the cheaper the electricity it produces, although larger reactors are arguably less safe than smaller ones. The largest nuclear power plant in the world currently is the Kashiwazaki-Kariwa Nuclear Power Plant. It has seven reactors in the gigawatt range, KK-1 to KK-5, which are boiling water reactors with an rated output of 1.067GW(e) each, and KK-6 and KK-7, advanced boiling water reactors each with rated outputs of 1.315GW(e). However these reactors and their associated fuel fabrication facilities have been plagued with problems including management malfeasance, falsification of data and earthquakes. All reactors are currently offline for inspection.
a reactor is the cheaper it can produce electricity though, and recent designs have be in the multi-gigawatt range.
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