What Will My Daughter Look Like? See Your Future Girl

A daughter inherits two X chromosomes, one from each parent, where a son gets an X and a Y. A father passes his single X to every daughter he has and to none of his sons — and that X is the one he received from his own mother, so a daughter carries a copy of her paternal grandmother's X.
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Having two copies leads to something no son experiences. Early in development each of her cells switches one X off at random and every cell descended from it keeps that choice, so she grows up a mosaic: some tissue running her father's X, some her mother's. The clearest illustration is a tortoiseshell cat, whose patches are two coat-colour alleles showing in different cells. In people the effect is subtler, but it is why a carrier of an X-linked trait can sometimes show it mildly or unevenly.
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Two X copies also keep recessive X-linked traits hidden. She would need the same variant on both chromosomes to be affected, so red-green colour vision deficiency reaches roughly 1 in 12 men but only about 1 in 200 women. Daughters are far more often carriers than affected.
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Height follows the same mid-parental method used for boys, reversed: subtract about 13 cm (5 inches) from the father's height, average it with the mother's, and most girls finish within roughly 10 cm either side. Her face, meanwhile, is polygenic — many genes each contributing a little, from both sides.

Often, but not as a rule — and the rule everyone has heard turns out not to hold. The claim traces to a 1995 study reporting that one-year-olds resembled their fathers more than their mothers, explained as a way of reassuring a father of paternity.
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It did not survive follow-up. Children tested at one, three and five showed no significant bias towards the father; a further pair of experiments came nowhere near reproducing the original result; and other work found children resembling their mothers more, or both parents equally. The honest summary is that daughters resemble both parents about as much as each other.
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What genuinely does make a daughter look like her father is ordinary inheritance: half her autosomes come from him, plus one of her two X chromosomes. A strong paternal resemblance is common for that reason — it simply is not guaranteed, and a daughter who takes after her mother's side is just as unremarkable.