Happy Vertical People Transporters were the Sirius Cybernetics Corporation brand of lifts in the Hitchhiker's Guide offices. Zaphod Beeblebrox encountered one of these lifts during his search for Zarniwoop.
They were given Genuine People Personalities, and were sentient enough to argue with people and to have "defocused temporal perception." The latter concept was intended to enable the lifts to see far enough into the future to arrive at a floor before a potential passenger realised they wanted a lift, thus saving them from having to wait around, chat and make friends like they would have to do normally.
The Happy Vertical People Transporters appeared in:
Behind the scenes
According to The Hitchhiker's Guide to the Galaxy: The Original Radio Scripts, the concept of sentient elevators came from Adams' time working the night shift at a Hilton; apparently, the lifts were automatic and stopped at every floor, so Adams would be sitting in front of the entrance to the lifts at 3 a.m. in the morning when one would come shooting down, open its doors for some 40 seconds, and then continue to the next floor down.