The exception is with highly parallelizable tasks, like fighting a war. But space exploration isn't that sort of job.
So, here's your list:
D-Day. Federal Highways. The National Park System.
Those are highly parallelizable tasks.
The internet and the Manhattan project are better examples, but it's debatable whether those things would be invented regardless of governments. They were a matter of time.
Now, about the Apollo project: Congratulations, we spent a Metric Boatload of money, and it got us what? A flag on the moon. Whoopie. The US also got to thumb their nose at Russia for a bit. That is not space exploration. That is the ability to convert a large quantity of money into a really expensive, one-time-use space car that was designed to stick a pole in the ground.
More upsettingly, the Apollo project undermined real space exploration for decades. There were some viable ideas about how this could be achieved. You may be as interested and as surprised as I was when I first realized this was true: http://www.spacedaily.com/news/nuclearspace-03h.html
Or you can dismiss this as readily as the rest of my comments. Either way, my new years resolution is going to be to swear off any kind of politics on any kind of online forum.