The Origin of Species
I'm pro half-elf and half-orc. IMC, elves (including Sea Elves), orcs, and sahuagin (who have throw-backs who look like Sea Elves) are all the same species as humans.
Elves are the First Born, like the Ancients in Stargate.
Humans are a partially fallen version, some more than others. We're the Homo Sapiens Neandertalis to the elves Homo Sapiens Sapiens.
Orcs and sahuagin are elves twisted by the evil magic of Morgoth, or someone similar, back in an age forgotten by man.
I don't like other half-races, with the exception of tieflings and aasimaar. Half-dragons, half-ogres, etc., strike me as way too high on the Cheese Factor rating.
As for hybrids not occuring in nature and always being sterile, I know of one exception: the red wolf of the American Southwest. It's unclear to scientists whether it's a subspecies of grey/timber wolf, or it's just a cross-breed of coyote. And it has a small, endangered, self-sustaining population, whatever it is.
Of the other near human "races", I think they are distinct lines of parallel evolution. and so cannot crossbred -- like the marsupial Tasmanian wolf, compared to any other wolf. Looks the same, has the same ecological niche, but it's utterly different genome, among other things being a marsupial instead of a mammal. I'd put goblins and lizardmen in that category.
For dwarves and gnomes, I'd say it's a different branch of evolution, like australopithecus afarensis (Lucy) compared to the Homo branch. I guess they are two different species of Dwarfopithecus, and can't interbreed, or maybe they just think its icky.
As for halflings, Homo floresiensis comes to mind -- the halfling-sized fossils found in Indonesia in 2004. So maybe they are just a different species of the Homo genus? But given early D&D's subraces of Tallfellow (halflings with elves characteristics) and Stout (halflings with dwarvish characteristics), plus Hairfeet (normal halflings), maybe halflings are the missing link, the common origin of the Homo line (elves, orcs, sahuagin, and man) and the Dwarfopithecus line (dwarves and gnomes).
Only elvish scholars would likely have figured that out, and they aren't likely to let the "First Born" tag drop.
