This paper categorizes some of the fundamental hopes and fears expressed in imaginings of artificial intelligence (AI), based on a survey of 300 fictional and non-fictional works. The categories are structured into four dichotomies, each comprising a hope and a parallel fear, mediated by the notion of control. These are: the hope for much longer lives ('immortality') and the fear of losing one's identity ('inhumanity'); the hope for a life free of work ('ease'), and the fear of becoming redundant ('obsolescence'); the hope that AI can fulfil one's desires ('gratification'), alongside the fear that humans will become redundant to each other ('alienation'); and the hope that AI offers power over others ('dominance'), with the fear that it will turn against us ('uprising'). This Perspective further argues that these perceptions of AI's possibilities, which may be quite detached from the reality of the technology, can influence how it is developed, deployed and regulated. A survey of 300 fictional and non-fictional works featuring artificial intelligence reveals that imaginings of intelligent machines may be grouped in four categories, each comprising a hope and a parallel fear. These perceptions are decoupled from what is realistically possible with current technology, yet influence scientific goals, public understanding and regulation of AI.