In Once More, With Feeling, Spike says, “Strong. Someday, he’ll be a real boy”, when he notices the strength of one of Sweet’s henchmen. This is a reference to Italian author Carlo Collodi’s children’s novel The Adventures of Pinocchio which features an animated marionette whose dream is to become human. The story was made famous by Walt Disney’s film Pinocchio.

In To Shanshu in L.A, Wesley realises that the Shanshu prophecy means that Angel will become human after fulfilling his destiny. The gang have the following conversation:

Wesley: “Well, it’s saying that it won’t happen tomorrow or the next day. He has to survive the coming darkness, the apocalyptic battles, a few plagues, and some - uh, several, - not that many - fiends that will be unleashed.”
Angel: “So don’t break out the champagne just yet.”
Cordy: “Yeah, break out the champagne, Pinocchio. This is a big deal!”

In Hellbound, Spike says,”To making me a real boy again?” - an echo of the comment he made in the Buffy musical. It’s also a Pinoccio reference. In Soul Purpose, Freds says that Spike, “Deserves to become a real boy.”
In Smile Time, Lorne says of the injured puppet-Angel, “Medic! Doctor! Is there a Gepetto in the house?” Gepetto was Pinocchio’s wood-carver father.