A programmer was a person who was specialized in creating and writing computer programs such as holographic programs.
In 2364, a series of malfunctions aboard the USS Enterprise-D – which were caused by a microbrain from Velara III – included locking two crewmembers in the head programmers' rest room. (TNG: "Home Soil")
When asking The Doctor in 2371 why he always had to say his line "Please state the nature of the medical emergency." when activated, he told B'Elanna Torres that he could only speculate about his programmer's motives. (VOY: "The Cloud")
The Doctor stated that his programmers haven't cluttered him with pithy Earth trivia. (VOY: "Persistence of Vision")
When Voyager discovered members of an alien species in hibernation, Harry Kim told the captain that they should have awaken four years ago but they are still inside a program. The programmers obviously wanted the people in the system to decide for themselves when it would be safe to come out. (VOY: "The Thaw")
In 2374, The Doctor offered the isomorph Dejaren to study and explore literature and art but Dejaren was confident his programmer's on Seros wouldn't allow that. (VOY: "Revulsion")
Furthermore, The Doctor told the EMH Mark II, that he was saving Voyager from annihilation when the Mark II was only a gleam in his programmer's eye. (VOY: "Message in a Bottle")
The Hirogen Donik was a programmer. (VOY: "Flesh and Blood")