Spaceman
The Space Shuttle was what remained after NASA's planned manned Mars mission was cancelled. The Shuttle was not originally intended to have as many flights as it did. NASA was extremely derelict to have eventually retired the Shuttle without having a replacement orbital-access vehicle available. As things stand now, NASA has to pay the Russians millions of dollars every time an American astronaut visits the International Space Station.
quantumclaustrophobe
There'd be a much smaller space station.
We might have had a fly-by of Venus or Mars by now.
It's possible there'd be a lunar base in operation.
CactiJoe
Fewer people would have died. We need to create the perfect inner space (on the Earth) before we waste trillions trying to get into outer space.
nineteenthly
The shuttle was incredibly far behind schedule and seems to have eaten money at a time when NASA wasn't getting enough anyway. The initial plan was to continue with missions to the moon, build space habitats and have a mission to Mars. This is what would've happened. Having said that, Apollo is very wasteful because it involves throwing away practically an entire spaceship the size of a skyscraper for a single mission.
Paula
We would have been able to go to the moon the whole time.
But people got bored with the few moon shots that we did have. And Apollo rockets are not suitable for putting people or other payloads into low earth orbit. It was designed for heavy payloads to go into high earth orbit (where the moon is).
But your question is one of "what if"
And sad to say we can not run the clock backwards and do things differently.
We stuck with the reality that it was 1972 when we last went to the moon -- 46 years ago.
People that are 45 years old or less simply were not even old enough to have experienced it.
It looks like we will rely on China or India to show us the way. China has a plan to go to the moon in the next decade.