With the Open Gaming Licensce, there's a huge array of new supplements and settings for d20. Some are more balanced (gameplay-wise) than others.
As for crossbreeding, its assumed creatures of the same type can hybridize (humanoids with humanoids, giant with giant) and may types of creature can successfully breed with just about anything (dragons or extraplanar, as both types are intensely magical). Some game settings state no crossbreeding is possible or the resultant children are sterile, like the mul half-giant from Darksun if my memory serves.
With undead that create spawn, such as vampires and wraiths, if the pregnant mother is killed by the undead there could be a possibility of her child being half-vampire or whatever. That's up to the DM as undead can't breed per se. They have no Constitution score and therefore no lifeforce. As beings of negative energy its nigh-on impossible for them to create life.
It is DM's call whether to allow hybrids. Blanket bans on half-breeds can fend off munchkinism but there are challenging role-playing possibilities in a character with a mixed background. Plus, some of the kids are so cute; for instance the trixie, a gnome/pixie cross.
Nihil est ab omni partum beatum.
(Nothing is an unmixed blessing)