In Mystery of the Emblem, several Dragonstones of various elements exist, including Fire, Earth, Flying, Ice, Mage, Divine, and Dark (Unused). Rather than being used as weapons, these stones function as items that transform their users into the dragon form that corresponds to the element in question (Eg: Firestone into a Fire Dragon), allowing them to maintain said form for a set number of turns. In these states, they use unlimited breath "weapons" that correspond to the dragon form that they assume. Enemy dragons operate slightly differently, remaining as dragons after using a stone for an unlimited amount of time.
In Rekka no Ken, there are no playable Manaketes (Ninian and Nils' Dragon forms are not playable), and thus, there are no actual Dragonstones existing within the game's data. However, Ninian and Nils retain their Dragonstones within the story, allowing them to transform at will.
In The Sacred Stones, Myrrh owns a Dragonstone that has 50 uses. This Dragonstone cannot be repaired by the Hammerne staff.
In Awakening, Dragonstones, along with Beaststones, are treated as weapons instead of items more than any previous game, complete with their own actual weapon category and weapon type icon, in addition to being assigned sets of technical stats.
In old development notes for Genealogy of the Holy War, it is mentioned that the sacred weapons are forged from Dragonstones. These notes also suggest that the Falchion from the Akaneia Series is forged from Dragonstones as well, but this element is not incorporated into the games involved. This idea contradicts the fact that Falchion is said to be fashioned from one of the fangs of Naga.
In Nah's S-rank support with Brady in Fire Emblem: Awakening, it is proposed that a Dragonstone could be used to transfer half of a Manakete's life force to a human, calling it the stone's "true power". However, Nah states that she had only heard this second-hand from Nowi, and admits that she does not know if it is true or not.