As SF Signal has been reporting, TOR books has been asking various authors to post about their favorite Robert A. Heinlein novel. This is to promote the release of the "first-ever authorized biography" of RAH. As opposed, I imagine, to H. Bruce Franklin's decidedly unauthorized Marxist analysis, Robert A. Heinlein: America as Science Fiction (1980), aka the book guaranteed to make Heinleinites wig out.
There have been some interesting responses, like Rudy Rucker's observations about some of his juveniles, Charles Stross providing a convincing reappraisal of Glory Road (1963), and David Brin maintaining his self-conscious political maverick pose by championing Beyond This Horizon (1948).
The thing to understand about RAH is both his novels and his career divide into two parts. In the first part of his proffessionsal life he wrote to order for legendary editor John W. Campbell, Jr. Campbell would assign RAH a plot and he would dutifully flesh it out into a rousing juvenile adventure. Later, in the 1960's, RAH began writing to his own preferences. He penned adult fiction often featuring a character that functioned as an Heinleinian mouthpiece who dramatized RAH's socio-economic ideas. So any appreciation of him has to take this split into account.
So what are my choices?
Time for the Stars (1956) is my favorite of his juveniles. It tells the story of two psychic twins, one who will travel on a relativistic spaceship to explore various solar systems, and the other who will remain behind in telepathic contact, functioning as an FTL radio receiver. The idea of a First Expedition was something of a cliché when RAH wrote this novel, but I didn't know that at the time, and besides, I like those kinds of stories. And this novel dramatized the twin paradox in a way that really stuck with me.
Of his later novels, The Moon is a Harsh Mistress (1966) is the one that impresses me most. Its retelling of the American Revolutionary War dressed up in spacesuits is entertaining, and the novel displays his right-populist, "Libertarian" politics in stark lines. This is the book from which the Libertarians took their political slogan "TANSTAAFL!" (Next we'll have a political movement that takes its ideas from comic books.) To complicate matters RAH has his lunar colonists involved in novel sexual relations that are likely to confound the "nuclear family" crowd. All in all it's an enjoyably thought provoking novel.