Comedy, Science Fiction
Depending on which you want to emphasize, you could call Hitchhiker's a comic science fiction story or a science fiction comedy.
Science Fiction
The science fiction part of Hitchhiker's Guide is pretty clear: this is a book about aliens and space travel and a planet that builds other planets to sell to rich people. (Currently, that is all science fiction. But soon…) We do think it helps to have some background in science fiction to get some of the jokes. For instance, as we note in our Shout-Out section, there's some joking about Star Trek; and as we note in Ford's character page, his entire character seems like a joke riffing on Doctor Who.
Comedy
There's a lot of stuff in Hitchhiker's Guide that makes us laugh. Some of the funnies come from Adams's tone and style. One thing we should note, though, is that a lot of the comedy here is kind of sad.
Comedies traditionally end with some happy event that makes everyone feel better—like a marriage. If you consider that something that will make you feel better, that is. Hitchhiker's comedy, though, is kind of dark: Earth is destroyed and never fixed, and not only does Arthur not find much enlightenment or happiness, he also has to face the idea that his life has been a total lie (he's not a human being—he's just part of a computer that a pair of mice bought). And at the end of the book, it's not like our heroes are not going on some great quest to fix the galaxy. They're just going off to get a bite to eat. This is comedy, but it's dark.
Parody? No, not really
Now, you might find people on the interwebs describing Hitchhiker's Guide as a parody, as if it's funny because it's making fun of other science fiction works. We disagree. Sure, it makes a few jokes about Star Trek and Doctor Who, but most of the humor comes from the absurd situations that the characters find themselves in.
In a parody, you have to know something about the original to get the joke. For instance, Weird Al's "Fat" is only funny if you know Michael Jackson's "Bad". In Hitchhiker's Guide, most of the jokes only rely on an ability to notice that things don't fit together: brainiac mice, depressed robots, a fjord-maker, and so on. So even if there are a few parodic moments in the book, the book as a whole isn't really a parody.