Science Fiction; Mystery
Well, the science fiction part is pretty clear: this is a book about an imaginary technology (humanoid robots) and how people deal with them. (This was even more science fiction-y when Asimov wrote these stories in the 1940s, before Honda had built ASIMO and Björk made this weird music video)
But we're also going to say that these stories are often mystery stories of a particular type. They're not crime mystery stories (although Asimov also wrote straight-up crime mystery stories). The mystery here tends to be a scientific mystery: given what we know about robots (the Three Laws), why are they acting the way they do? Notice also that many of these stories share something in common with mystery stories, like the Sherlock Holmes mystery stories: the story only ends after the great detective (here, usually robopsychologist Susan Calvin) explains the mystery's solution to us and the other characters. Because we are as clueless as Watson.