Fubblegum

Fubblegum is the het ship between Finn and Princess Bubblegum from the Adventure Time fandom.

Canon
Finn had a crush on Princess Bubblegum since the very beginning of the series, however, he didn't admit it until the episode "Wizard Battle".

When Princess Bubblegum was physically 13 in "Too Young", she had feelings toward Finn. However, she didn't seem to like Finn in any other episodes. and sometimes she even feel awkward about Finn's attempt to pursue her.

In the episode "Incendium", after being rejected by Princess Bubblegum again, Finn felt upset and lay on the floor, while holding a chunk of her hair he got from the episode "To Cut a Woman's Hair". In "Burning Low", Finn thought that Princess Bubblegum was jealous of Flame Princess, and when she tried to reason with him, Finn thought Princess Bubblegum is playing him, and then finally admitted to Princess Bubblegum that he used to have a crush on her.

In "The Pajama War", Princess Bubblegum was hanging out with Finn, and Finn was acting chill and didn't think about her the romantic way. After that, Finn didn't seem to like Princess Bubblegum romantically again, and their friendship became more stable since Finn no longer had a crush on her.

In series finale "Come Along with Me", Princess Bubblegum kissed Finn, but not romantically. After the main series, Bubblegum is living with Marceline, and Finn and Huntress Wizard are still keeping in touch, as seen in "Fionna and Cake".

Fanon
Fubblegum was very popular in the early seasons of the series. However, sometime after "What was Missing", the popularity of Bubbline surpassed Fubblegum. One of the reasons why people don't like Fubblegum is the age gap between two characters, since Princess Bubblegum is way older than Finn.

Trivia

 * Princess Bubblegum actually kissed Finn more than she kissed Marceline on screen. In total, Princess Bubblegum kissed Finn 4 times ("Too Young", "Wizard Battle", "The Real You" and "Come Along with Me") on screen, while she only kissed Marceline 3 times (one time in "Come Along with Me", 2 times in "Obsidian") on screen.