I'm about half-way through Walter Issacson's Einstein: His Life and Universe. I recommend it to anyone who wants to see just how messy and (dare I?) indeterminate real science is done. It's like making sausage.
The misperception that real science is systematic, deliberate and businesslike often taught in schools seems almost like a conspiracy to dissuade students from thinking at all. (Maybe it is!)
Connections was terrific. James Burke was both informative and playful at the same time. I especially remember the whimsical transitions. And Bill Bryson’s book A Short History of Nearly Everything is a good book to start with, too.
For somewhat more, um, erudite believers, try The Pleasure of Finding Things Out by Richard Feynmann.
Knowing the people who made for us the world we live in were, well, people, I think encourages other people to give it a go, too. Before they were august figures in history, back when they were actually doing their work, great scientists were just, you know, some nerdy guys. (Except for, you know, Marie Curie. She was just some nerdy girl.) What are you? Maybe there’s a cool idea in your head that, like Einstein or Newton, just needs to be worked out.