Blasphemy was something that was seen as being offensive towards a god or a religion as a whole.
According to the Vulcan Elder it would be blasphemy to enter the reliquary in the catacombs beneath the monastery at P'Jem. Following the discovery of the secret listening post beneath the sanctuary this claim was considered wrong. (ENT: "The Andorian Incident")
In 2265, a changed Gary Mitchell assured fellow esper Elizabeth Dehner that she'd enjoy being a god, denying that his statement was blasphemy. (TOS: "Where No Man Has Gone Before")
In 2369, Q told a seemingly-deceased Jean-Luc Picard that Q was God, to which Picard scoffed. Q referred to this as "blasphemy", remarking that Picard was fortunate he did not cast him away or smite him or "something". (TNG: "Tapestry")
That same year, Vedek Winn Adami accused Keiko O'Brien's secular teachings of the Bajoran wormhole and the Prophets as being blasphemous. Later, a member of a crowd that followed Winn said that Benjamin Sisko would "pay in eternity for his blasphemy". (DS9: "In the Hands of the Prophets")
In 2376, "Father Mulligan" (The Doctor) called Seamus's attempts to use hypnosis on him "blasphemous". (VOY: "Spirit Folk")
In 2401, due to anti-Kolinahr demonstrations which occurred on Aklion VII, Vulcans refused to go there, proclaiming such a visit to be blasphemy. (PIC: "Dominion")