Although everything, including pairings, in Vocaloid is purely fanon, the most popular heterosexual ships seem to be Gackupo/Luka, Kaito/Miku, and Len/Rin.
Miku/Luka is the most popular homosexual pairing, having had albums full of songs about their love. Yaoi fans, however, tend to gravitate towards Kaito/Gakupo.
In the album In the Aeroplane Over the Sea by band Neutral Milk Hotel the narrator often alludes to Anne Frank. Fan interpretations include the pairing of Jeff Mangum, the writer and singer of the album, with Anne Frank and the belief that Jeff actually is in love with her. The lyrics, many of them sexual in nature, seem to be the main reason people come to this conclusion.
The two main characters played by Ellie Goulding and Calvin Harris from "Outside" music video are prominently shipped together because their other major collaboration "I Need Your Love" featured the two characters (also played by them) as an adorable couple as well as Goulding and Harris's real life friendship.
From the famous children's group The Wiggles, Emma and Lachy take this Up to 11. They hid their relationship for two years, but in those days, even the children started to see something spark between them. Now they are engaged and married.