Because of the common genetic ancestry throughout the Milky Way Galaxy, by way of the ancient humanoids, many species were able to interbreed with or without the help of genetic technology. (TNG: "The Chase")
There can be unexpected consequences to interspecific relations and as such, it was a researched topic. Ktarian Doctor Mizan, an expert in interspecies mating practices, known for his "empirical research." (TNG: "Timescape") Starfleet Academy had a semester on interspecies protocol, as well as Starfleet's handbook on personal relationships that was three centimeters thick. (VOY: "The Disease")
One should note that there can be certain difficulties involved in reproducing between species, even humanoid, for anatomical reasons; for instance, not all species keep their genitals in the same place (Star Trek VI: The Undiscovered Country), or incompatible number of required genitals (DIS: "Choose Your Pain"), or the embryo will not survive to term due to genetic or physical reasons, such as life-threatening birth defects or dangers to the mother during birthing which may require caesarean section or fetal transport to save one or both. Following the birth of the Ktarian / Human hybrid Naomi Wildman, The Doctor noted that "there's no sign of any interspecies abnormalities." (VOY: "Deadlock")
Seska believed that Cardassian / Human cross breeding was possible, as she attempted to have Chakotay's child. (She did nevertheless proved that a Cardassian / Kazon hybrid was possible.) (VOY: "Alliances", "Basics, Part II") Gilora Rejal made the same assumption when she expressed an interest in reproducing with Miles O'Brien. (DS9: "Destiny")
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Background information Edit
According to the original script of TOS: "Who Mourns for Adonais?", interbreeding between Humans and the Greek god species was also possible, as Carolyn Palamas got impregnated by Apollo. However, this was cut from the actual episode, but was later used in the Star Trek: New Visions comic Of Woman Born.