Their Germans are better than Our Germans

That's what President Eisenhower was supposedly told when he asked about why the Russians were ahead in the space race. ( Source : entry for VfR )

There was a joke going around after the shock of Sputnik in 1957 -- the President of the United States called in his experts and asked ``What happened? How did the Russians get so far ahead of us in rocket technology?'' His advisors answered:
``Their Germans were better than our Germans.''

This was mirrored in the Movie The Right Stuff when the Russian Grand Designer said "Our Germans are better than their Germans.".

Anyway, the contribution of the German Rocket Scientists and Engineers to the space programmes of 3 nations - the USA, USSR, and oddly enough, France, is revealed over at the Encyclopedia Astronautica. As is how the UK managed to lose a golden opportunity. :

Von Braun led a group of 108 leading engineers who chose to surrender to the Americans...
[...]
29 of the team moved to private industry in the United States, 21 returned to Germany. A few new engineers were recruited from Germany, having stayed behind to complete war-interrupted education.
[...]
There is no complete documentation, but at least 234 rocket engineers and technicians went to the Soviet Union

The largest contingent, over 129, worked in Filial 1 of NII-88, creating rocket designs in competition with those of institute leader Korolev. They also provided advice to the Russian engineers ordered to copy the V-2 rocket. 23 others worked within Glushko's OKB-456, transferring V-2 propulsion technology and building a subscale prototype of the advanced engine that would later power Soviet ICBM's. Small groups of others were working in other design bureaux and offices of the Aircraft Ministry, transferring technology related to other specific missiles or rocket aircraft.
[...]
The British staged an enormous effort in firing three V-2 rockets from Cuxhaven in Cuxhaven in 1946, then lost all interest in pursuing ballistic missiles until the mid-1950's. By late summer 1945 some two hundred Peenemuende scientists, 200 V-2 firing troops, and 600 ordinary POWs were transported to Cuxhaven. Upon arrival, they were split into two groups and interrogated. The information given by each group was then compared to ensure inaccuracies and deceptions were eliminated.
[...]
After this event, the British government lost all interest in ballistic missiles. Some of the leading experts they had detained were employed by the French. It was only in the late 1950's that Britain decided to pursue a ballistic missile, the Blue Streak.
[...]
The V-2 launch bunker at Wizernes had been dynamited by British commandos on 9 May 1945 in order to keep the French from ever being able to put it to use. The French began to recruit German experts then working for the British at Project Backfire at Cuxhaven. By 15 May 1946, Herbert Weiss had convinced 35 German engineers at Cuxhaven to 'defect' to the French. Others soon followed, signing contracts to work in France. By October 1946 the French employed nearly 90 German experts, working in groups at Emmendingen and Puteaux in the French zone.

There's more, with many more links, over at Slashdot.

Lest anyone think this is all Ancient History, there's this:

Baum and Groettrup's engine and rocket designs led directly to the Soviet R-7 ICBM. This awesome rocket started the space race, and is still in use today as the Soyuz 11A511U space launcher.
[...]
Although many of the German team were laid off in 1952 and returned to Germany, others, notably Bringer, continued to work for LRBA and its successor organisations, developing the Viking 2 engine that would power the Ariane.

And the Canadian Arrow X-Prize contender is basically a crewed V2.