Right, well the Adventure Time fandom - among all fandoms - is full of people who enjoy pairing off two plus characters together and stand by that pairing. This is called "shipping".
There are many different kinds of shippers, and I wish to talk about them.
The oldest ship to exist on Adventure Time has to be "Fubblegum". This is the nickname for the pairing of Princess Bubblegum and Finn. The current Canon Status of this ship is Dormant, and it is currently inactive. It is Critical on the side of Princess Bubblegum due to her not having any known feelings for Finn, but on Finn's side we do know that he still holds some feelings for Preebubs. We don't know if or when he will act on these, though I sense they may cause conflict somewhere down the line due to him currently being in a relationship with Flame Princess. There's also the chance that if he does start chasing after PB again she'll spot that and call out his bullshit, or any other character may do the same
The Fubblegum Fandom used to be flourishing due to it being a Canon Ship, but it started to become skeptical in Season 3 with it being pointed out significantly that the crush was unrequited (as well as the anti-PB movement starting in the fandom)', and then finally there was a Mass Ship Migration upon the airing of Incendium where Finn went into heartbreak over PB's "rejection" and Flame Princess was introduced with the announcement that Finn "had a new crush". Many old Fubblegummers are now in the Righteous Flame fandom. The remainder left behind include younger, more casual viewers (many rebelshipping due to not understanding what is wrong with the age gaps) and some older, long-term viewers who appreciate the nostalgia of the more classic episodes. Bear in mind, this ship is actually very unpopular in the PB fandom due to her lack of want for it.
Then we have "Finnceline". This is the act of pairing together Marceline and Finn. The status of this ship is "Completely Friendzoned", although that doesn't exclude the possibility of it being brought up again in future.
Finnceline started off as a competitive ship to Fubblegum when Finn and Marceline's relationship was strengthened in "Henchman" and "It Came From The Nightosphere". Marceline's popularity grew RAPIDLY, and her bond with Finn was interesting to the fandom, so there was this impression that Finn would eventually "realise what's better for him and ask Marceline out" or something. There were shipping wars between the Fubblegummers and Finnceliners. But since the "Go With Me" troll, Finnceline has been critically impacted and not many people can hold a strong argument for it anymore.
Okay, thirdly we have the "Righteous Flame" ship - FPxFinn, of course. The current status of this ship is Canon, with some Obstacles rising up in the form of three things: Flame Princess's Instability, Flame Princess's Alignment, and Finn's remaining feelings for Bubblegum.
The massive Righteous Flame Fandom is filled largely by Fubblegum Shipjumpers as well as Fubblegum Rejectors, or rather it USED to be when it was new, and is seen as a Companion Ship to Bubbline below. Currently most new fans appreciate Righteous Flame as a ship although they aren't necessarily devoted to it. There isn't much to talk about with the Righteous Flamers, apart from that its more devoted fandom seem to be Anti-PB in the same way the Fubblegum fandom is Anti-FP, and this causes conflict between the fandoms as we have seen numerous times here on the Wiki.
The final Major Ship I'll talk about is called "Bubbline/Sugarless Gum", and it is the act of shipping together Princess Bubblegum and Marceline. This ship's status is currently Subtext Dependant Ex-Canon and it is based on subtexts in the episode "What Was Missing" that suggested that it's possible PB and Marceline were in a past romantic relationship. This was boosted by the controversial "Mathematical!" recap which HIGHLIGHTED this possible subtext to the audience, although the recap is illegitimate to the AT crew and was taken down for "offering only one interpretation". However, this doesn't necessarily mean that nobody shipped this until the controversy - there was also some shipping going on after the episode "Go With Me".
The Bubbline fandom seems to be the largest as of right now, on par with the RF fandom, and it completely owns the website of Tumblr although it is less popular on the Wiki. The fandom is largely filled with older viewers, including civil rights activists who believe strongly a step needs to be made in promoting a decent LGBT pairing on childrens' television, as well as many LGBT fandom members themselves who appreciate there is something they can possibly relate to on the show. The Bubbline Fandom is also filled with Marceline fans and Third-Way Rebelshippers who reject any chance of a Love Triangle around Finn and thought instead "let's ship the two girls together instead of either with Finn". The Bubbline fandom seems to have incorrect notions about character roles, though, and there is conflict within itself as to what these might be.
And now the Multishippers. These are usually also Crackshippers, people who pair together any old character if it looks or sounds funny, and Multishippers are okay with several potential relationships and would be okay with however it turns out.
Multishippers generally avoid fandom wars due to lack of motivation of supporting a single side, and they usually have the most Unbiased Perspective - that is to say, their speculation on character interaction is not blinded by shipping biases, so these usually cross over with Roleplayers and Analysts. A multishipper can write more in-character than most strong monoshippers. It seems that most Multishippers do actually find themselves attracted to Finnceline, oddly, as they conclude that the Finnceline ship is the most "Ideal" with the personalities and they are not barred by the friendzone.
Other notable factions include Analysts, people who look at characters and their interactions and determine how they are developed, what their personality is like and how they would behave, as well as Petrikovians - people who feel massive pity for the character Simon Petrikov and enjoy reblogging fanart of him and talking about his relationship with Marceline more than they enjoy talking about any other character (possibly even Ice King included). Analysts may become Ship Neutral, whereas Petrikovians may become IK shippers due to their pity for the character.