If I mention science fiction and hybrids in the same sentence, chances are this may be the first thing that comes to mind:
As "fascinating" as Spock may be, he's not a natural hybrid; it required a team of Vulcan scientists to create him. Given how different Vulcan and human metabolisms are, it would have been impossible for his parents to conceive naturally. However, closely related animal species can and do produce hybrids. According to this article in the New York Times, up to ten percent of animal species and twenty-five percent of plant species interbreed occasionally with a different species. Some of these hybrids are obviously different from their parents; they may have an intermediate number of teeth, for instance, or their coats may be a patchwork of their parents'. (See the article for a picture of a zebra-horse hybrid called a zorse.) Unfortunately, due to genetic issues such as an unusual number of chromosomes, hybrids tend to be sterile. (This is more of an issue in animals than in plants.) Although hybrids generally can't compete against their parent species in the same niches, sometimes they are able to find a unique niche where they thrive and the parents don't.
What does this mean for science fiction? For near-future science fiction, I could see interest in creating species better suited to handle upcoming climate change. Perhaps scientists would even find ways to make these hybrids fertile by manipulating genes and chromosomes. Although species have to be very closely related (usually within the same genus; never outside the order) to hybridize in nature, genetic engineering makes it possible combine DNA from vastly different species. (I think in this case, probably only a few genes would be added from the other species, not half.)
Nearly all life on Earth uses the same genetic code (there are a few exceptions in extreme climates), but would this extend to life on other planets? Even if extraterrestrial life follows the same biochemical principles that we do, tiny but crucial details may be different. Their equivalent of DNA would be highly unlikely to follow our genetic code, or perhaps they may use different amino acids to build proteins. But if there's a way to create terrestrial-extraterrestrial hybrids, science fiction writers will find it--and explore the results and implications.