In 2151, Doctor Phlox advocated denying treatment to the Valakians for their genetic disease to Captain Jonathan Archer. He believed that the Menk, who co-inhabited Valakis, were on the verge of an "evolutionary awakening", and that they would be interfering with a natural process if they saved the Valakians. (ENT: "Dear Doctor")
Bele had once heard that people on some Federation planets believed that they were descended from apes. In 2268, Spock clarified to him that "the actual theory is that all lifeforms evolved from the lower levels to the more advanced stages." (TOS: "Let That Be Your Last Battlefield")
In the 24th century, an increasing number of the Zalkonians began experiencing isoelectric bursts in their bodies which were the result of evolutionary changes. They were changing into powerful Non-corporeal lifeforms. (TNG: "Transfigurations")
In late 2369, when Vedek Winn Adami demanded that Keiko O'Brien stop teaching the Bajoran wormhole as a scientific phenomenon, Keiko asked what would happen when it came time to teach evolution or the creation of the universe. Winn replied that those "issues" would be dealt with when they arose. (DS9: "In the Hands of the Prophets")
In 2370, Lieutenant Commander Data speculated that a strange contagion that had overtaken the Enterprise-D was "de-evolving" the crew, by activating introns that reverted them to earlier evolutionary forms. (TNG: "Genesis")
Ronald D. Moore commented, "Trek [...] accepts evolution as a believable and valid theory. Gene [Roddenberry] himself felt this very strongly and although we do try to embrace many points of view and many beliefs, there are some matters on which we do make our feelings known. That said, I also think that anyone within the Trek universe who espoused a 'creationist' or similar view as to the origins of life would find their beliefs respected – 'respected' being fundamentally different than 'believed.'" (AOL chat, 1997)
TNG: "The Chase" revealed that most, perhaps all, humanoid species in the galaxy descended from an ancient species, with it being stated these beings had seeded their DNA on a number of planets. The Klingons and Cardassians rejected the idea they could have a common ancestor with either one another, Humans or the Vulcans/Romulans, while the Humans and Romulans accepted this.
Human evolution was indirectly referred to in an ultimately unused line of dialogue from the script of TOS: "Court Martial". The line was said by Samuel T. Cogley after he realized that the reason Jame Finney had tried to pardon James T. Kirk from being accused of the murder of her father, Benjamin Finney, was that she had known her father was actually still alive. Theorizing that she had known this due to instinct, Cogley remarked, "Thank God there's that much of the animal left in us."