It's hardly appropriate for HN, but I wonder how differently the world would look if NASA had received a much larger budget. Probably taken from the US Military's allocation, how much would the loss of half of the US Navy have affected world politics and conflicts? Or what would the USA look like without the Iraq war of 2003 onward?
(I'm trying to be as neutral as possible in my language here, I don't want to start a flamewar about US and geopolitics!)
I doubt we'd have gotten further into space as some of us would like, but I do think we'd have already proven that asteroid mining can work, and some people would be living multi-year tenures on the Moon. Whether we'd have bootstrapped our way to mining and using nuclear materials in space is doubtful, but certainly possible. (in other words, building nuclear rockets that have never been close to Earth's biosphere, which would open up large parts of the Solar System for human exploration)