The Tempest is, along with Hamlet, clearly one of my favorite works by Shakespeare. Perhaps I am a bit biased since I got to play Prospero for a while (Act 4), but there is something about that play that I find attractive. As in many Shakespearean works, the humanity (the human quality) of the characters strikes me.
The Tempest is the story of the "magician" Prospero, his daughter (Miranda), his slave (Caliban), and the son (Ferdinand) of his enemy (Alonso, King of Naples), who has fallen in love with Miranda. A ship carrying Ferdinand, his father, Prospero's brother (who overthrew him) and several others is caught in a storm, the result of which is that all these characters are thrown overboard and wash up on an island (in several different groups) - the same island inhabited by Prospero and his young daughter (and their servant/slave, Caliban).
It turns out that Prospero brought them to the island (by way of his "airy spirit" Ariel) to exact his revenge. In the meantime, Ferdinand runs into Miranda, and they fall in love. Caliban comes across Trinculo (a jester) and Stephano (a drunken butler), and among other things (such as being drunken fools), they plot to overthrow Prospero. We then come to the 4th act, in which Prospero gives Miranda to Ferdinand and puts on a marvelous, magical spectacle (with the aid of his servant Ariel). The old man then remembers Caliban and company ("I had forgot that foul conspiracy / Of the beast Caliban and his confederates"), halts the festivities (confusing Ferdinand and Miranda in the process) and gets off his famous lines "We are such stuff / As dreams are made on; and our little life / Is rounded with a sleep." At the end of the 4th act, Prospero (with Ariel's help) chases off the three rogues.
We move to the 5th act, in which Prospero plans to take his revenge upon the King and the Duke (Propero's brother) for mistreating him in the past, but has a sudden change of heart:
Ariel: [...] your affections Would become tender. Pros: Dost thou think so, spirit? Ariel: Mind would, sir, were I human. Pros: And mine shall.
So it is that we experience The Tempest as a romance; neither a comedy nor a tragedy, but one of Shapespeare's plays (including A Winter's Tale) that has the potential and the momentum to end tragically, but for a sudden, changed heart and the rediscovery of reason and human kindness.