It is widely assumed that researchers must normally secure informed consent from participants if research is to be ethical. But what exactly are people being asked to consent to? Most obviously, it is to supplying, or providing access to, data; but are they also agreeing that this data can be used in any way relevant to the research, or do they retain a right to control its use? A third question is: are they consenting to themselves being included within the focus of study, so that asking for consent amounts to assigning a right not to be researched? A further question concerns whether there can be group rights not to supply data, to control the use of data, and/or not to be researched? Such claims have been made by spokespersons for the disabled, indigenous groups, commercial organisations, governments, and religious cults. Justifications for these various rights usually appeal to the principle of autonomy, in one form or another. Yet this principle, being universal, must also apply to researchers themselves. So, does this imply that researchers have a right to carry out research? As this makes clear, there are conflicting rights-claims around research. This paper will examine these and their implications.