I'm aware that all of the bachelor and bachelorette NPCs in Stardew Valley have various cut-scenes, which get triggered as you increase your relationship status with them (and based on location). But which of the other NPCs have their own cut-scenes? The only one I've seen so far is Linus (I've triggered two for him). Are there others?
Most definitely! If you have a relationship status with them, there will be a condition for you to have a cut-scene or mailbox interaction with them.
The following non-marriageable Villagers will each have significant involvement in a cut-scene you can experience:
Caroline, Clint, Demetrius, Emily, Evelyn, George, Gunther, Gus, Jas, Jodi, Kent, Lewis, Linus, Pam, Pierre*, Robin, Shane, Vincent, the Dwarf, Krobus, and the Wizard.
That leaves the following NPCs as without cut-scenes or only rewarding you with mailbox rewards for their relationship:
Gil, Marlon, Marnie, Morris, Willy, Mr. Qi, and Sandy.
Note that the cut-scene with Gunther will be unlocked once you donate enough Artifacts.
*: Pierre's cut-scene at 6 hearts is fantastic.