Genetic engineering

Genetic engineering is the practice of manipulating the DNA of a living organism, usually through the use of cloning.

Pre-Federation Earth
Some of the earliest genetic engineering performed on Earth was by Dr. Sarina Kaur of the Chrysalis Project, who created augmented humans. These individuals -- including Khan Noonien Singh -- brought about the Eugenics Wars of the late 20th century, and as a result, human genetic engineering was severely limited by subsequent law. (novels: Star Trek: The Eugenics Wars)

Human genetic engineering remained controversial into the mid 22nd century, when Dr. Arik Soong stole a number of frozen Augment embryos preserved following the Eugenics Wars. He brought them to term and raised them through early childhood, until he was arrested and imprisoned. To his dismay, however, his "children" displayed many of the same antisocial tendencies as their predecessors. (ENT episodes: "Borderland", "Cold Station 12", "The Augments")

By the 22nd century, Adigeon Prime became a destination for humans seeking illegal genetic modifications. 

Several early Earth colonies continued to practice genetic engineering, even centuries after the formation of the Federation. (novels: Star Trek: The Eugenics Wars; ; )

The Federation
Some genetic manipulation was still allowed to treat serious birth defects, but large-scale "eugenic" procedures were outlawed. Still, as late as the mid 24th century, illegal procedures were still being performed. When it was discovered that Julian Bashir had his genetic abilities enhanced by doctors at Adigeon Prime at age five, he faced possible dismissal from Starfleet, though ultimately his father, Richard Bashir, agreed to a prison term. 

Other Races
The Denobulans practiced genetic engineering of their own species, though they managed to avoid the problems faced by humans. 

The Klingons attempted to build on the work on human augmentation to improve their own race. The results were deadly, and ultimely led to a widespread alteration of the Klingons' physical appearance. (ENT episodes: "Affliction", "Divergence")