We can consider ways in which a given individual, A, might have been different. In many cases such thoughts indeed preserve the identity of A: he might have been born in France, for example if his mother, pregnant with him, had gone to France. But the thought that he might have had different parents altogether (i.e. different from the ones he actually had) seems no longer a thought about A: we are now considering a different person. What underlies this common-sense distinction? An influential view is that the identity of an individual is given by the particular gametes from the union of which that individual is formed. The paper considers: (a) the motivation of the view; (b) its consequences, particularly for population policy, in utero damage and genetic defects, and rights which are possibly associated with these matters; and (c) its problems, particularly with genetic repair and monozygotic twinning. The paper discusses the merits and the dangers of supposing that the common-sense distinction is conventional or baseless; and the related question whether increased understanding of the genome should make us think in terms of types rather than individuals.