Genetic engineering was a process in which the DNA of an organism was selectively altered through artificial means. Genetic engineering was often used to produce "custom" organisms, such as for agricultural or medical purposes, as well as to produce biogenic weapons. The most common application of genetic engineering on intelligent beings in the Federation was corrective DNA resequencing for genetic disorders. A far more dubious application of genetic engineering was the genetic "enhancement" of individuals to produce improved senses, strength, intelligence, etc.
Human
During Earth's 20th century, efforts to produce "superhumans" resulted in the Eugenics Wars. Genetically engineered individuals such as Khan Noonien Singh attempted to seize power. (TOS: "Space Seed")
This would lead to the banning of genetic engineering on Earth by the 22nd century, even research which could be used to cure critical illnesses. This ban was implemented because of the general fear of creating more tyrants such as Khan. It was also felt that parents would feel compelled to have their children genetically engineered, especially if "enhanced" individuals are allowed to compete in normal society.
Some, including geneticist Arik Soong, argued that it was simply convenient for humanity to denounce the attempts at genetic "improvement" of humanity, that it was inherently evil because of the Eugenics Wars. He argued that the source of the problem, in fact, wasn't the technology, but humanity's own inability to use it wisely.
Imprisoned for, among other crimes, stealing the embryos of a number of Augment children, Soong wrote long treatises on the subject of genetic augmentations and improvements. His works were routinely taken and destroyed by his jailers, until the intervention of Jonathan Archer, after which they were taken and stored.
Archer expressed his hope to Soong that research into genetic engineering that could cure life-threatening diseases would someday be resumed.(ENT: "Borderland", "The Augments")
Others, however, chose to establish isolated colonies as became the case with the Genome colony on Moab IV, which was established in 2168. It became a notable and successful example of Human genetic engineering in which every individual was genetically tailored from birth to perform a specific role in society. (TNG: "The Masterpiece Society")
By the 24th century, the United Federation of Planets allowed limited use of genetic engineering to correct existing genetically-related medical conditions. Persons known to be genetically enhanced, however, were not allowed to serve in Starfleet, and were especially banned from practicing medicine. (TNG: "Genesis", DS9: "Doctor Bashir, I Presume")
Nevertheless, some parents attempted to secretly have their children genetically modified. (DS9: "Doctor Bashir, I Presume") Unfortunately, most of these operations were performed by unqualified physicians, resulting in severe psychological problems in the children. (DS9: "Statistical Probabilities")
In 2377, The Doctor performed prenatal genetic modification on Miral Paris to correct a spinal deviation, a congenital defect that tends to run in Klingon families. (VOY: "Lineage")
Dominion
The Founders of the Dominion performed extensive genetic modifications on their two servant races, the Jem'Hadar and the Vorta, in order for them to better serve their roles and to ingrain a fanatical devotion to the Founders. (DS9: "The Abandoned", "Ties of Blood and Water") As a result of these modifications, neither species reproduced in the traditional biological sense. (DS9: "To the Death")
According to Vorta legend, they were originally ape-like creatures who were gifted sentience by the Founders. (DS9: "Treachery, Faith and the Great River")
The Dominion also genetically engineered biological weapons, such as the blight they unleashed against the people of the Teplan system. (DS9: "The Quickening")
Suliban
During the 21st century, the Suliban were no more evolved than humans. However, a number of Suliban, from a faction known as the Suliban Cabal, became recipients of some very sophisticated genetic engineering thanks to a mysterious humanoid from the 29th century. These "enhancements" included subcutaneous pigment sacs, a bio-mimetic garment and eyes with compound retinas – which allowed them to see things starship sensors likely could not detect. The Suliban considered these "enhancements" as "progress". (ENT: "Broken Bow")
Klingons
Others
When they were captured by a pre-warp civilization in 2152, Jonathan Archer and Malcolm Reed claimed to be prototypes of a new breed of supersoldiers. (ENT: "The Communicator")
Genetic engineering had been employed on Denobula since the twentieth century, to generally positive effect. (ENT: "Borderland")
The Tosk were engineered by the Hunters to be prey for their traditional hunts. (DS9: "Captive Pursuit")
The Brunali were proficient at genetic engineering, which they used to create modified crops capable of surviving on their Borg-devastated homeworld. However, they also genetically engineered some of their children to produce a pathogen deadly to Borg. These children were then allowed to be assimilated, so that they could spread the infection to their Borg vessels. Icheb was one such child. (VOY: "Child's Play")