I wonder, if a Dark Elf and a Breton have a child, what race would the child be? I'm wondering this because in Morrowind, I'm wondering whether my Breton character should have a child with a certain Dark Elf?

Child shares therace of its mother and some traits of father, this rule still applies to everyone and that includes Bretons ( and excludes Septims , sometimes, maybe..)

Pretty much what Cryticus said. Children inherit traits from both parents just as in real life like eye color, body type, dispositions, etc. The only real determining factor is the mother's race which is reflected in her children. So assuming that the father is a Dunmer and the mother is a Breton, the child would be a Breton with some Dunmeri traits like maybe paler-than-average skin, shaper features, and a predilection towards Conjuration magics and fire compared to the average Breton. Karliah in Skyrim shows this best by being a Dunmer with blue eyes from her non-Dunmeri father.

The others have already summarised things for you, but here is the http://www.imperial-library.info/content/notes-racial-phylogeny-and-biology.