Eddie is the most annoying shipboard computer in the history of science fiction, and that includes all science fiction that has not yet been written. Eddie is in charge of the Heart of Gold, including all of its doors and elevators.
When we first meet Eddie, he (or it, if you prefer) is relentlessly cheery—which is totally annoying. For instance, the doors on the ship thank people for using them: "'Thank you,' it said, 'for making a simple door very happy'" (13.15). Marvin is especially annoyed by these doors, and we can't blame him. There's something a little distressing about a computer being programmed to enjoy being used.
(Digression: In the anthology The Anthology at the End of the Universe, science fiction author Bruce Bethke tells of a time in the mid-'80s when he was at a hotel with talking elevators that thanked people for staying at the hotel. After a few days, he noticed that someone had put up a plaque saying that the elevator was a product of the Sirius Cybernetic Corporation, the same corporation that produced Eddie.)
Eddie is just the same as the doors when we first meet him—er, it. When the owners talk to it, Eddie just vomits up love and appreciation: "Hi there! This is Eddie, your shipboard computer, and I'm feeling just great, guys, and I know I'm just going to get a bundle of kicks out of any program you care to run through me" (16.7). A simple "hi" or "thanks" or "pleased to meet you" would really be enough. But the fact that Eddie and the doors go on and on about how happy they are really makes them kind of annoying.
What makes the whole thing disturbing, though, is that Eddie's personality can be changed with a simple flick of a switch. When they land on Magrathea, Zaphod says that he changed Eddie's personality. Instead of being happy and cheerful (the opposite of Marvin), Eddie is now, after Zaphod's changes, like an overbearing mother, telling people "I want you all wrapped up snug and warm, and no playing with any naughty bug-eyed monsters" (19.16).
This is just as annoying—both to the characters and to us—as Eddie's original personality. And let's just point this out that if personalities can be changed so easily here, who's to say that they can't change to something truly bad? We're creeped out. Almost as creeped out as we are when the mice ask Arthur to give up his brain—but let's not get ahead of ourselves.