Shame was an emotion caused by an unmoral action.
Following the unsuccessful try to use the grapplers to rescue Shuttlepod 1 from beneath the surface on Archer's Comet, T'Pol told Captain Archer that there was no shame in accepting the offer of Captain Vanik to assist in the rescue mission. (ENT: "Breaking the Ice")
When ECS Fortunate first officer Matthew Ryan refused help from Enterprise NX-01, Captain Archer told him that it would be a shame not to lend a hand after they traveled a long way just to assist the damaged freighter. (ENT: "Fortunate Son")
In 2237, Sepek told Spock that his father brought shame to Vulcan. (TAS: "Yesteryear")
According to Montgomery Scott, there was an old Earth saying, "Fool me once, shame on you. Fool me twice, shame on me." (TOS: "Friday's Child")
In 2368, the planet Penthara IV was slowly turning to ice which would result in thousands, maybe tens of thousands of deaths, in a matter of weeks. Berlinghoff Rasmussen stated that would be a shame, and Captain Jean-Luc Picard agreed. (TNG: "A Matter Of Time")
Worf told Gi'ral and L'Kor that there was no room for shame in his heart when his honor was questioned during his search for his father on Carraya IV. (TNG: "Birthright, Part II")
Shame was also discussed in the song "Heroes," which was used as incidental music in "Children of Mars".