Adventure Time has a lot of talk about relationships and mild-to-moderate sexual innuendo.
Characters kiss on the mouth, on the cheek or (rarely) with tongue.
Butts are seen throughout the series.
Some characters position themselves and speak sexily sometimes.
Women in bikini is seen sometimes.
Finn had a crush on Bubblegum.
In the episode "What Is Life?" a brief scene shows the Ice King (a character that liked kidnapping princesses) reading what appears to be a nudie magazine on his bed. There are also heavy undertones of procreation in this episode, including claims that the Ice King's lightning bolts made him the "father" of a robot they revived.
In "Burning Low" Jake explains to Finn the "15 Tiers" of a relationship by saying: "Bro, you gotta let things take their natural path. Look, look, let me explain some junk about dating. Right now, you're at Tier 1, which is hugging. But pretty soon, you'll be at Tier 2, which is smooching. Then down the road, you'll make it to Tier 5, where she'll let you discover all fifteen feet of her loong, beautiful stomach. Then after awhile, you'll make it to Tier 8, where you touch her horn for the very first time. Very special." Finn asks "What about Tier 15?" and Jake gets mad and shouts "You stay away from that! Do not do Tier 15!".
In one episode, Finn's clothes are incinerated off of him (we see his butt for an extended time). A character comes over and tells him, "Hey naked kid".
We see Finn in his underwear in one episode (they were torn off and stolen by a girl; the scene is comedic, not sexual).
Some characters put spaghetti on another's mouth in some episodes; this is somewhat suggestive.
In one episode, Finn and two other people are naked with logs covering their crotch. The log moves up and down as the characters walks or move. The original design had beavers instead of logs, but this was changed due to CN censorship.
In one episode, Cake increases in size and explicitly shakes his giant butt.
In one episode, Finn sees a female getting into a shower and gets flustered, however nothing is seen.
Jake made a "special" video for his girlfriend Lady Rainicorn as seen in "The Pit". In one episode, she's pregnant, and in another episode we see their five children.
Finn and Jake play to put the finger in things in one episode.
In the episode "Blood Under the Skin", Finn crosses the Swamp of Embarrassment, where there are a lot of curtains with a lot of people having a shower and with their parts covered (some offscreen). Finn is called a pervert and he repeats that he is not, and a man says "My most private parts seen by a boy!" and "my privates!", that are said twice in that episode. At the end he comes completely embarrassed with a red face.
Finn tells Mrs. Cow to take the paper bag off her udder. A blue bird and Mrs. Cow take the paper bag off her udder, but it's actually revealed to be an udder with a face on it.
Lady Rainicorn and Jake is set-up for "seven minutes in heaven" by Finn. He places them inside a closet.
On the gender-switched episode, Prince Gumball takes Fionna to his bedroom, which showed rose petals on the bed, and he was about to remove his shirt, but it was actually the Ice Queen taking off her cover and wanting to destroy her.
Ricardio the Heart Man threatens to cut out Bubblegum's heart and make out with it. He is also an implied rapist.
In the Tree Fort where Finn and Jake live, can be seen on a wall a ripped image of an apparently naked woman. However, according to a crew member of the show, it represents "a woman in a crappy snapped bikini".
The creator of the show, about a character's design: "Marceline's dad, when he turned into a giant monster, we had a bunch of notes about it, that it was too vagina-like. We had to change the shape of it and then they said it looked too much like a penis."
Some lines of the show includes: "I'm helping you by tempting this guy with... my body... ", "Alright, I'm 13, she's 13. Have fun. Be yourself.", "Ice King is the hottest hottie!", "Okay, but I'm gonna kick your butt. Not that I'm thinking of butts...", "Oh my glob, you're touching my woman body!", "I'm actually a virgin queen bee.", "You'll put cards in your mouth?!", "Only good babies get sassages.", "You wanna go inside, bounce around a little?", "My body isn't hot anymore!", "Or... maybe they kissed so much they passed out!", "I know all about your dirty deeds. Now it's Lumpy's turn to slump those lips! Bring it in, baby.", "Now you can partake of my pollen crumbles and become my drone.", "Why do my parts hurt?", "I missed you at nights." or "I will never know the pleasures of skinny dipping.". Worth mentioning that some of the sentences are said by "thematic" characters.
A song contains these lyrics: "I'm busy, makin' babies, greasy babies, sliding on my gravies". Another contains these: "Shake your extremities / (...) All your arms and knees / I want 'em, shake 'em, baby, please / Baby, shake your eyes for me. / (...) Quack me up with some yokes / I like girls who know the ropes... " Another contains the line "I can introduce your parts to something new."