I wonder how many authors set out to write trilogies. Tolkien, for instance, intended the Lord of the Rings to be the first big ass volume of a two-volume set (the second being the equally big ass The Silmarillion), as well as the sequel to The Hobbit. His publisher sensibly refused to do this, instead dividing up LOTR into three books. On the opposite end of the spectrum, Peter Jackson took The Hobbit (which would have made a fine two and a half, possibly three hour movie) and created a cinematic trilogy padded with action scenes destined to become amusement park theme rides.
"Star Wars," to use another cinematic example, was originally a standalone movie, the perfect hero's journey complete with fairytale ending. It didn't become a trilogy (and then an intended ennealogy, which Wikipedia assures me is the correct term for a series with nine entries) until the original movie broke box office records. If the first movie had bombed, there would be no "Luke, I am your father" spoiler, those of us with the hots for Han Solo could tell ourselves Luke won the princess's hand, and there would be no Jar Jar Binks. On the other hand, we would not have the description "Han in Carbonite" as convenient shorthand for a cliffhanger ending in the second book of a trilogy.
Good world building and/or a compelling cast of characters can translate into a successful multiple volume book series. A lot of authors write each one as a standalone so no matter which book in a series a reader picks up, there are relatively few spoilers and a satisfactory -- and complete -- story arc. Each book in a continuing series moves the characters forward, relationships progress, and there's often unexpected reappearances from other characters - often antagonists -- assumed dead or defeated -- but every book ends with that world's equivalent of the One Ring being tossed into the volcano. In your face, Sauron! Readers don't have to wait until the next book to find out if Han gets defrosted.
With a trilogy, there is an overall story arc and/or unifying theme that carries through all three books. In ones with continuing characters, smaller quests may be wrapped up at the end of each one, but the main "hero's journey" or story arc is not completed until the end of the third book. Even more irritating, the second book often ends with a cliffhanger, which can be really frustrating when you know you have to wait for another six months to a year to find out what happens. I personally get a bit cranky when I'm made to wait, but when the books are just that good... the waiting makes the eventual gratification that much better.
Some people view cliffhangers as a deliberate ploy to get readers to buy the author's next book. Well, of course we want you to read our next book, but it's rarely that Machiavellian. Often it's as simple as having to stick to an allowed word count, which doesn't always allow for a neatly wrapped up ending. And with or without cliffhangers, f you don't want to read the next book in a series, be it a dualogy, trilogy or whatever-the-hell-ology, the author isn't doing his or her job.
Which leads me to my favorite seven trilogies. These books hooked me from the start, with worlds and characters that I've revisited more than once since the first reading. Please keep in mind these are my personal favorites, ones from my childhood onwards! If yours aren't listed here, please feel free to chime in and recommend them.