A lot of people have commented about this remark of yours. I'm old enough (barely) to remember Gagarin's first venture into space (I distinctly remember live TV coverage of the launch of John Glenn's first American orbital space launch) and I have never forgotten about Gagarin, nor about Valentina Tereshkova,
http://en.wikipedia.org/wiki/Valentina_Tereshkova
whose flight into space, the first by a woman by a large number of years, was just in the news on its fiftieth anniversary. A sufficiently old American grew up in the Space Age, and remembers the names of all the space pioneers.
If younger readers of Hacker News would like to move their minds back in time to learn more about (the American phase of) the early age of manned space flight, I recommend the documentary movie In the Shadow of the Moon,
http://www.imdb.com/title/tt0925248/
which I watched with my children just yesterday evening. There is, alas, little mention of the Soviet space program in the film, because the focus is on manned missions to the moon, but the interviews with surviving astronauts are fascinating, and the film-maker does a good job of setting the historical context.
I'm aware of this because my grandfather hand engraved the medal.
We were taught that the Russians made it to space before we did, and I think that's about it before we moved on to American achievements. Perhaps I had a nationalistic teacher.
The one personal note I liked to add: I got to meet half a dozen astronauts and cosmonauts (picking them up from the airport and bringing them to our museum for a conference). Every single one of them emphasized that, even as the two sides were competing and treating each other as mortal enemies, those who were actually going to space viewed one another as friends or even brothers.