Wendip is the shipping of Dipper Pines and Wendy Corduroy. It is one of the more popular pairings in the fandom, and has the most canonical basis.
Canon Evidence Edit
For most of the series, Dipper canonically has a very obvious crush on Wendy. He has difficulty speaking properly to her, blushes around her, and goes to great lengths to spend time with her -- examples being creating an incredibly lengthy plan full of unnecessary details just to start a conversation with her, creating over ten clones to make sure said plan goes smoothly, and going back in time over and over again until he creates an incredibly intricate plan that will ensure a timeline where Wendy and Robbie don't begin dating.
Dipper has also shown obsessive tendencies towards Wendy besides his overly intricate plans to spend time with her, such as keeping a box full of pictures of her, being unable to sleep if he's thinking of her, and so on. In the fandom, his infatuation is regarded as cute and endearing.
In Blendin's Game, Dipper and Mabel travel ten years into the past and run into young Wendy and Tambry. Young Wendy whispers something to Tambry, and then Tambry says to Dipper "My friend thinks you're cute." This shows that young Wendy had a crush on Dipper/thought he was cute.
Wendy pretends not to notice Dipper's feelings up until season 2 episode 2, Into the Bunker, where Dipper finally confesses his feelings. The two have a talk towards the end of the episode, and Wendy admits she always knew how he felt, but doesn't reciprocate his romantic feelings, stating that the two are too far apart in age. Even after being rejected, Dipper still has lingering feelings for Wendy until episode 15 roadside attraction.
However, the two are still incredibly close friends. Wendy deeply treasures Dipper as a friend, and in Weirdmageddon Part 3: Take Back the Falls, tells Dipper he means a lot to her, and switches hats with him. She gives him a letter and tells him to "read it when (he) misses Gravity Falls", which contains signatures of all Dipper and Mabel's friends from Gravity Falls. Wendy and Dipper have a very meaningful friendship, and even if Dipper is unable to date her at this point in time, he still cares for her immensely, and regards her as the "coolest person he knows."
Due to Dipper's endearing infatuation and devotion to Wendy, fans enjoy the idea of Wendy having a change of heart and reciprocating Dipper's feelings towards her and agreeing to date him. Dipper is usually shown to be very awkward, taking a mathematical or logical approach to a relationship, but having Wendy there to mellow him out and take things as they are. On the other hand, fans are content with Dipper's one-sided pining.
It is also popular for fans to age up Dipper to an age where it wouldn't be as taboo or questionable for Dipper to date Wendy, and the two eventually start going out after remaining close friends for many years.
There is also a sexual take on the ship, where Wendy and Dipper are portrayed as doing sexual things in secret. Dipper's pubescent age and hormones often come into play here, as he is developing sexual urges and lustful thoughts. It is canon that Dipper has 'weird internet history', and in his Reddit AMA, Bill reveals that his internet history mostly consists of pictures of redheads.