It didn't occur to me to pick the Roman empire, because I thought the OP meant "countries" that are a little more recent. While what PJ says about one country (or person) building on the achievements of its predecessors is true, the Roman empire does stand out for the enormity of its own contribution- arguably moreso than the Greeks, the British or Luxembourg.

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As for the moon landings, no offence intended, but I think it's a little short sighted to measure its significance by the returns it has brought so far. I do think that human space travel (in our own solar system, that is) is going to be enormously important in the far future; and I'm sure that future generations will look on the 20th century space race as an important phase in history.