In Ender's Game, is Ender genetically engineered (along with Peter and Valentine) or are they just naturally gifted?
Genetic engineering, also called genetic modification, is the direct human manipulation of an organism's genetic material in a way that does not occur under natural conditions. It involves the use of recombinant DNA techniques, but does not include traditional animal and plant breeding or mutagenesis.
If I recall correctly, Ender's parents were assigned to one another, so he was the result of a breeding program, but not genetic engineering.
To clarify apoorv020's answer, Ender's parents were two unusually gifted people.
The story arc (in "The Polish Boy" and "Teacher's Pest" short stories from "First Meetings" collection) is that Ender's father John Paul was a genius little boy in a non-compliant (>2 kids) family in Poland.
When young Captain Graff was assigned to try and get the kid into Battle School after he was accidentally discovered during IF testing, John Paul said that he would agree to consider going in exchange for his whole family being moved from Poland to USA. John Paul never intended to go to orbit anyway. Graff knew that, but explained later that he was playing a game of chess - John Paul would have a child some day, who'd inherit his genes, AND would be perfect age for when they needed their genius commander; whereas John Paul himself would be too old.
When in the University in USA, grown up John Paul meets Theresa Brown - the brilliant daughter of a major military genius who's in opposition to IF due to disliking population control laws. John Paul falls in love with her, as Graff had originally intended (since they match perfectly), and Peter, Valentine and Andrew are the result.
They actually suspected it was part of Graff's plan when they met:
"And here's a thought," she said. "What if this is their plan?"
"Them. The same them we've been talking about. What if the reason they didn't send you back to Poland is because they wanted you to marry a really smart girl—maybe the daughter of the world's leading military theoretician. Of course, they couldn't be sure you'd end up in my section of Human Community."
"Yes, they could," he said thoughtfully.
"Ah," she said. "So you didn't want my section."
He stared at the remnants of the food. "What an interesting idea. We might be somebody's idea of a eugenics program."
And, Graff as good as admitted it at the end of "The Polish Boy":
"If we have more time before we need our commander," she said, "then do we have time for him to marry and have children and then the children grow up enough to be the right age?"
"Just barely, yes. We have just barely enough time. If he marries young. If he marries somebody who is very, very brilliant so the gene mix is good."
"But you aren't going to try to control that, are you?"
"There are many steps on the continuum between controlling something and doing nothing at all."
So, as apoorv020 said, definitely not genetic engineering but you could consider it selective breeding.
Directly? No. Both Ender's parent are somewhat religious and where probably opposed to this kind of modification. It's also said in one of the book of the Shadow series that Ender was conceived before his birth has been authorized/ordered by the authority, so any modification are improbable in is particular case.
All three children are shown to have inherited the intelligence of John Paul and his wife Theresa, though there are hints throughout the Shadow series that they may have also been genetically enhanced.
-- Wikipedia article about Ender's father
I will leave the "part of a breading program" to DVK how explain it better than me in his answer.
Ender is clearly part of a eugenics program; that his parents received permission for a third child is evidence that the powers-that-be felt him genetically likely to be of benefit.
Likewise John-Paul being permitted to move to the US despite being part of a non-compliant family indicates some eugenic potential.
But calling a eugenics program genetic engineering stretches the term.
It's possible, and implied, that Ender may have been retrovirally altered, but that, also, isn't genetically engineering the affected individual, but augmenting them... I'm not convinced Ender was augmented, however. I am open to the idea that Peter and Valentine were augmented in utero...
This quote from Ender in Exile shows that if he was engineered, he didn't know about it.
“Oh,” said Abra. “So that’s not what he really was.” “No, Abra,” said Ender. “We really are what our genes make us. We really have whatever abilities they give. It’s what we start with. Just because his genes were shaped deliberately, by a criminal scientist, doesn’t mean they’re any less his than our genes, which are shaped by random selection between the genes of our father and the genes of our mother. I was shaped deliberately, too. Not by illegal science, but my parents chose each other partly because they were each so brilliant, and then the International Fleet asked them to have a third child because my older brother and sister were so brilliant but still were not quite what the I.F. wanted. Does that mean that I’m not really me? Who would I be, if my parents hadn’t given birth to me?”
And as it seems that Graff didn't hold back information from Ender after he left Eros, he probably would have told Ender about that.
Is the Wiggin predisposition to military genius a natural genetic one, or was it altered in some artificial way?
When authorizing Ender to be born, did the IF use genetic manipulation or genetic screening, assuming they were choosing from a pool of zygotes? How could the IF be sure that Ender would be the perfect mix of Peter and Valentine?
Orson Scott Card: The IF was not sure Ender would work out well. Peter and Valentine came so close, and were so off-the-charts excellent on some vital measures, that the IF thought the odds were very good that a third child from the same parents would be suitable for command.
The only genetic manipulation was that the IF suggested Ender’s parents time the conception in ways that increase the prevalence of Y rather than X spermatozoa, because a male child would be more likely to have the aggressiveness that Valentine lacked.
(Ender's World: Fresh Perspectives on the SF Classic Ender's Game)