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John von Neumann created an early form of a computer that contained three components that were to become commonplace in all computers - a CPU, a fast-access storage area, and a slow-access but larger storage area. (The storage areas are analogues to RAM and a hard drive today). The machine would fetch instructions to perform, one at a time. The machine was the Maniac I, built in 1952.

Today, any machine that operates in this same, sequential manner is referred to as having von Neumann architecture.

He also developed the idea of the "Universal Constructor". It was a machine that combined a turing machine, and a mechanism for manufacturing. This machine would be able to accept a program that would describe itself, then, in two phases, make a copy. The first phase would involve physical construction of the copy, and the second phase would be tranferring a copy of the description into the new machine.

This machine is still too advanced for today's technology, but the idea has merit. Such a machine is often proposed as a cheap way to mine or colonize the entire solar system or galaxy. (see von Neumann probe)

Oddly, the first fictional use of the idea was in the short story "Autofac" by Philip K. Dick, published in 1955, which actually seems to precede John von Neumann's original paper about self-reproducing machines.

Transhumanist Glossary, http://www.aleph.se/Trans/Words/v.html
Lycos Webpedia Tech Glossary, http://webopedia.lycos.com/TERM/V/Von_Neumann_machine.html