1.2: Ariel enters at Prospero's command and hails him as his great master. He clearly is eager to please Prospero, but has a creative spark all his own, which is tied to the natural world. He wishes to fly, swim, dive into the fire, ride on the curled clouds. Whatever is asked of him, he'll apply his nature to it.
1.2: Ariel follows his master's instructions to every detail, and takes the form of fire on the sinking ship. He delights in his own personal touches about the whole "rack and ruin" thing, and is glad to report that everyone seemed mad with desperation, but that he also saw to it that not a hair on a single person was harmed. He gently placed everyone down on separate parts of the island, as his master wished, but with his own bit of flair.
1.2: Ariel is saucy for the first time, but not at all rude. He says that, since Prospero does give him pains, he'd like to remind him of the promise made that hasn't yet been fulfilled. Ariel thinks of his liberty, and in the meantime has dotted every "i" and crossed every "t" of his master's instructions, with no lies, mistakes, or grumblings.
1.2: Ariel listens to Prospero's angry words as his master recounts in full detail how Ariel came to be locked in a tree, and how he was saved, and what he owes, etc.
1.2: Ariel attends patiently to Prospero, promising to do all his bidding and so forth.
1.2: After Prospero promises to free Ariel in two days, the spirit is pleased as punch and eagerly asks what he can do.
1.2: Ariel, coaxing Ferdinand to come see Miranda so the two will fall in love, plays a beautiful little tune. It soothes Ferdinand about his father's death and also makes him curious. Later, Ariel sings a little rhyming song that is easily one of the most beautiful bits of verse on the block (if the block were the canon of Western literature).
2.1: Ariel breaks up the plot to murder the King with another little verse, commenting to himself about his master's wisdom in seeing his project through.
3.2: Ariel, invisible, enters in on the conversation between Caliban, Stefano, and Trinculo. Then he does his tricksy spirit bit, as he whispers "thou liest" to the air. He lets Trinculo get beat up for it, having his own fun while defending his master.
3.3: Ariel takes the frightening shape of a harpy, and gives an impressively scary speech to warn Alonso, Sebastian, and Antonio that they face judgment for their terrible crimes and intentions.
4.1: Ariel is summoned to help Prospero bring the Roman gods (or their shapes) to perform for the young lovers. He doesn't complain, and instead says he'll be quick as a wink. He ends with an eager "Do you love me, master? No?" and obviously gets a warm response.
4.1: Ariel reports to Prospero that the drunkard traitors, Caliban, Trinculo, and Stefano were led on by his music, and he's deposited them in a pool smelling of "horse piss" outside his master's cell. A job well done. He takes great delight in seeing the hounds chase after the drunkards.
5.1: Ariel reports on the three royal traitors: Alonso, Antonio, and Sebastian. He says their states are such, and the charm so good, that if Prospero saw them now, his affections would become tender. Prospero's all "Really?" and Ariel's all, "If I were a human, I would totally have feelings, and they would be warm fuzzy feelings, even towards mine enemy." Having influenced Prospero to have mercy, he goes off to fetch the traitors.
5.1: When the sailors get back, the boatswain reports that their boats are good as new. The men, well rested, have been lured forth to this place to meet their friends and bring the good news. Ariel reports shyly to Prospero that he has done all this (even more than he had been asked to do).
5.1: Ariel, before he is freed by Prospero, delivers his final line of the play: "Was't well done?"