Voyage, by Stephen Baxter
Wow. This is a very, very good treatment of space history... that never happened. It imagines a world where 1) JFK was invalided out of office (Jackie died in Dallas) and 2) Apollo only went to the moon 3 times AND 3) NASA shifted to a MARS mission after Apollo (partly because JFK off-scene was urging it on) - targeting a landing in 1986.
Baxter cleverly weaves lots of historical details together to present a plausible story AND explore the meaning of space exploration - he looks at the effects such missions have on the people involved and the costs to those committed to the journey. A might-have-been that has you saying "oh, I wish it had" AND "I'm glad it didn't" happen this way. Great science, great story.
I liked the moment when the Mars-bound ship uses Venus for gravity-assist, and the scientist on-board gets a few tantalizing observations, all the while thinking how a much cheaper unmanned craft could exhaustively radar-map Venus (which REALLY happened with Magellan)