Spongebob and Patrick of SpongeBob SquarePants, to the point where the show had a huge LGBT fanbase claiming their relationship was a real gay one (and some anti-gay groups, for other reasons). Canon-wise, it reached its apex with "Rock-A-Bye Bivalve", an episode where they raised a baby scallop together, acting very much like a married couple (with Spongebob as the housewife and Patrick as the deadbeat dad). At the end, when the scallop flies away to live on its own, Spongebob remarks how that is the hardest part of a parent's life. Patrick responds with a seductive "Yeah...let's have another."
The episode "Artist Unknown" had Spongebob's explanation of his piece in a one-on-one art class taught by Squidward:
Spongebob: [Showing his origami piece.]] That's you on the bottom. ... [Showing his "Rippy Bits" art.] You're on top this time.
Not to mention him going all sparkly eyed when he found out Squidward was the art teacher "You are the teacher?! To my pupil?! This isn't art class, it's heaven!"
"If I'm lucky, Mr. Talent will rub his tentacles all over my art."
A more recent episode (20,000 Patties Under the Sea) involving Patrick and Spongebob having to deliver patties to new customers had the two drifting off in a mini-submarine waving farewell to Mr. Krabs and Squidward. Spongebob enthusiastically says goodbye to Squidward seductively while twiddling his fingers in a feminine manner. Patrick points out that "You said 'Bye Squidward' twice." Spongebob responds "I like Squidward." in a gleeful way.
I don't even want to guess how far it'll go in the upcoming episode guest-starring Johnny Depp. From the preview already:
Patrick: I kind of like staring at him... [to Depp's character]
The commercial for that episode was more than just speculation, too. 
Not to mention the entire scene when that happens. Depp's character's overly-long surfboard comes out of the shack first, very slowly. Squidward out of nowhere, while watching it, um, grow, says, "Oh...my...gah-" and then faints. The Narrator describes the "really really big" surfboard slowly and with much relish, coming out of the house in a very position. All three characters are quite awed.
"That's No Lady", full stop. First of all, there's the obvious fact of "Patricia" attracting Mr. Krabs and Squidward before dropping a Bridget on them, but there's also the fact that Spongebob apparently has a detailed schedule of daily activities to do with Patrick, including "Stare at Patrick". It's heavily implied (and outright stated after Patrick dolls himself up and he and Spongebob go walking together) that Patrick is Spongebob's supposed girlfriend. Not to mention at the end when Patrick tears off his disguise leaving him in the nude, Spongebob hugs a naked Patrick, takes out the schedule, and tells him "Hey buddy, what do you say we go home and get started on this list?" They then happily run out of the restaurant towards Spongebob's home.
"Spy Buddies". When Patrick gets two-way radio pants, Spongebob goes right up to Patrick's butt crack to talk to Mr. Krabs. Then, the radio pants asks for a coin like a pay phone. Then, Spongebob raises a hand with a quarter and he and Patrick smiles.
For those of you who didn't get it, coin slot is a word for butt crack. Brain Bleach is available in that vending machine.
Karen: Henchmen. You know, big strong muscular men who do whatever you say.
Plankton: I like the sound of that.
Does anybody remember the opening to "Chimps Ahoy". Y'know, the one where Spongebob gets that backscratcher. And starts scratching his back. While moaning. With music straight out of a porn video playing. Then Patrick gets a turn. And it turns out that he was using Spongebob's arm. So, consider this. If Freud Was Right, and that backscratcher was a synonym for a 'prosthetic pleasure device' and Patrick ended up using Spongebob's arm, then does that mean...
"The Fry Cook Games", in which Patrick and SpongeBob grow ridiculous muscles, wrestle (and end up in very suspect positions), realize what they're doing to each other, hug, and then walk off hand-in-hand in the sunset together. While still sporting said muscles.
It gets worse: the fight climaxes with both characters trouser-less, standing in their underwear. Patrick's underwear just happens to be yellow and Spongebob's underwear just happens to be pink. So, metaphorically speaking...you do the math.
"These were white when I bought them."
"And now for our final event... Bun Wrestling!"
"Can You Spare a Dime?": When Squidward takes advantage of Spongebob's hospitality after getting fired, he has Spongebob serving him food in a maid's uniform. One that, oddly enough, has no back.
And Spongebob kisses him goodnight on the nose, then saying, "Goodnight, my little angel." And he spoon-feeds Squidward; and when yelling at him to finally "Get a job!" he straddles him in bed and gets close to his face while doing so.
Spongebob even stated in this episode he and Squidward are like brothers.... only closer.
In a recent episode, after receiving a written customer order, Spongebob takes the paper and gently caresses the side of Squidward's face with it. Just imagine it is as a feather instead and shudder...
"The Two Faces Of Squidward" was a non-stop Ho Yay fest when Spongebob accidentally slams a door in Squidward's face causing him to become handsome and everyone in town, man and woman, follows him around wanting to look upon his handsomeness, and acting like crazy stalkers. There's also SpongeBob's obsessive worry over Squidward's recovery. As well as Spongebob telling Squidward after his face changes the first time "You might even be more handsome than before. If that's even possible!" and calling him a "hunk".
Spongebob: "Oh, Squidward, I love you no matter how many times we smash your face!" (flops face-first onto Squidward, hugging him)
Squidward: "I almost wish that meant something." (Squidward does not object, and in fact is smiling)
The episode "Giant Squidward" has a scene where Spongebob and Patrick share the same ice cream cone, both licking it rather exuberantly.
The Valentine's episode has Spongebob trying his darndest to think of the perfect way to "show his love" to Patrick... which involves him creating a giant chocolate heart-shaped balloon for him (with a picture of Patrick on the front of it) and having them watch it from the top of a Ferris wheel at a Valentine's Day Carnival. However, when Sandy is late getting the balloon to the carnival and Spongebob has to give Patrick a "friendly handshake" instead Patrick reacts with great disappointment and reacts like a psychotic jealous boyfriend upon finding out how many people had gotten valentines from Spongebob. As a result, he goes on a unstoppable rampage around the Carnival, and when the chocolate balloon finally arrives he calms down, happily bites into it and tells Spongebob (who are both now covered in chocolate) "Aww Spongebob you didn't have to get me anything."
Patrick: *throws a guy to the side in anger* "PATRICK NEEDS LOVE TOO!!!!"
Patrick: (to Spongebob) "You broke my heart! Now I'm gonna break something of yours!"
The episode "Dear Vikings" has Spongebob kiss Squidward on the nose.
"Slide Whistle Stooges" has Spongebob and Patrick tie each other up in a rather big knot.
"Spongicus" has Spongebob a little to eager to feed the sea lion the sausages that are around Patrick's neck.
"He just wants the plump, juicy, warm, succulent sausages around your neck!"
In "Model Sponge", Patrick's suggestion to get Spongebob out of his depression is to sit down and drink some "Liquid Sausage".
In "Greasy Buffoons", Patrick can't stop licking Greasy Spongebob. OK, you can argue that he only wanted the grease, but still...
In "The Splinter", Squidward gives Spongebob an order card that reads, "Spongebob: 2 Krabby Patties. PS, You're an idiot. Love, Squidward." Spongebob giggles and says, "Love you too, Squiddy!"
In "The Smoking Peanut", where Patrick is "on the case" of who upset the Oyster, and the clues lead to Spongebob, Patrick states "I am so close, I can almost taste it" and then licks what appears to be the side of Spongebob's face, but is actually a popsicle.
"Squid's Visit" has Spongebob's obsession with Squidward become flanderized to the point that he becomes insanely stalker-ish in getting Squidward to come to his house. He goes so far as to steal Squidward's vacuum cleaner and turn his own house into an exact replica of Squidward's. You even have Sponge breathing heavily, looking at Squidward through the window while they're on the phone when Squid says he's coming over to get his vacuum back.
The entire episode "Squid In Love" was one huge dab of this for Spongebob and Squidward since Spongebob dressed in drag and acted like a lady towards him as a "pretend date" since Squidward is trying to learn how to date someone he loves. Spongebob is shown to clearly enjoy what he's doing. There is also the ending with Patrick dressing in drag.
"Trenchbillies". Spongebob and Patrick show the Trenchbillies Jellyfishing, and are dancing around singing. Spongebob than says "Now Patrick!" and they both lunge at each other with the tip of an iceberg, resulting in an accidental kiss.
"Sponge-Cano". Spongebob saves Squidward's life, Squidward's house gets destroyed for the nth time. And when Squidward mourns not having a house...
Spongebob: Well, I wouldn't say that... [cut to Spongebob and Squidward sharing Spongebob's bed. Spongebob gleefully flicks Squidward's nose.]
Squidward: Go away. [switches off the lights; the episode ends]
"Sun Bleached" might have the best example of this. At the beginning of the episode, Patrick wears Spongebob as a swimsuit.
"Naughty Nautical Neighbors" is an early example where Spongebob and Patrick fight over Squidward. You could probably get away with saying it's innocent until it reaches the infamous "Hey buddy, I warmed it up for you." scene with Patrick sitting naked in Squidward's tub. Then Spongebob pops in. "Rubber bath toys" indeed.
Can't forget when he calls Patrick his "ex-best friend" or when Squidward uncomfortably tells Spongebob that they are Just Friends.
The "Christmas Who?" special. When Squidward comes into their house, Spongebob very happily sings, "Hey Patrick who's that under the mistletoooe?"
"I'm Your Biggest Fanatic" - Patrick spots a guy in a jellyfish suit: "Wait, Jeffery Jellyfish! I have to touch you!" And at the end, Patrick can be seen dragging a rope-bound Jeffery away to Neptune knows where... "C'mon, Jeffery..."
There's also Spongebob's obsession with Kevin.
Welcome to the Chum Bucket has Mr. Krabs losing Spongebob's contract in a bet with Plankton, resulting in Spongebob working at the Chum Bucket. Cue a song Mr. Krabs and Spongebob sing about each other that sounds more like it's between Star-Crossed Lovers!
Mr. Krabs: I would trade it all away, if you'd come back to stay!
Spongebob & Mr. Krabs: This kitchen's not the same without you!
And then there's the episode "Sailor Mouth" where Spongebob writes on a dumpster: Squidward smells...GOOD.
From "Graveyard Shift": Squidward saying while hugging SpongeBob because he's terrified of the Hash-Slinging Slasher "SpongeBob, no matter what I've said, I've always sort of liked you!"
Earlier, in the German dub, when Spongebob is excited about the 24 hour shift, he exclaims, "Oh, that's romantic!"
"Fools in April" also has Squidward admitting he likes Spongebob in a crucial moment, but this time he does it because he feels so badly that he thinks he's hurt Spongebob's feelings. His anguished profession of an apology goes through a list of things he specifically likes about Spongebob. He goes into no details about anyone else.
"Alright, alright, I'm sorry, I'm sorry, I admit it, I'm sorry! I didn't mean to hurt you Spongebob, in fact, I LIKE you! I like living next door! I like hearing your foghorn alarm in the morning, and your high-pitched giggling at night!"
The episode "Dumped" where Spongebob is heartbroken after Gary (his pet snail) leaves him for Patrick is treated as if Spongebob and Gary were lovers until Gary eloped. And then at the end Gary goes back to Spongebob and Patrick acts as if Gary left him for another lover and screams (while in his underwear no less) "Gary, I thought what we had was SPECIAL!!!!"
The episode where Spongebob and Plankton become friends and Plankton becomes nicer and Plankton reveals he was just faking Spongebob acts like Plankton left him at the altar. "How long were you planning on doing this?! TELL ME!"
By the way this is when SpongeBob discovers Plankton with a Krabby Patty, and the entire reaction plays like a woman who encounters her husband when she hears he has beenCHEATING ON HER WITH ANOTHER WOMAN NO LESS.
In "Bummer Vacation", Spongebob became crazy that Patrick has his job and waits in his house. Patrick finds him in a corner and asks him if he's okay. Spongebob turns around immediately and walks creepily towards him, one can interpret it as of though Spongebob was going rape him.
Then there's this quote:
Spongebob: "I'VE BEEN WAITING FOR YOU PATRICK!"
All of "Boating Buddies". It starts with Spongebob searching for the source of a "noise", and upon reaching the silent Squidward, claims it was his breathing. After a chase that gets Squidward assigned to boating school, Spongebob adheres to Squidward's side, stares at him with huge eyes while breathing in heavy glee, strokes him with a loving two-fingered caress, and even draws a big "Spongebob + Squidward, Boating Buddies 4-ever" picture on the chalkboard, complete with hearts!
Spongebob's last line at the end of "Are You Happy Now?" when he finally gives Squidward a happiest memory. Which involves destroying a bunch of papier-mache Spongebobs.
Spongebob: "He's so handsome."
In "Extreme Spots", Patrick sang this line when he and Spongebob were jump-roping to show they were "extreme".
Patrick: "I try on his (Spongebob's) clothes while he's asleep in bed."
In Employee of the Month:
Squidward: Flowers and chocolate for you, Mr. Krabs!
An activity in an issue of Nickelodeon Magazine has you pairing up members of the cast as dancing partners. You pair up Spongebob and Sandy, Patrick and Pearl, Mr. Krabs and Ms. Puff, and Squidward and Plankton.
A very early example: In "F.U.N.", when Spongebob is chasing Plankton, who had just run off with a Krabby Patty, Spongebob chases after Plankton using a propeller to fly away. Spongebob takes a policeman's baton and spins it around, flying into the air. The cop's reaction is to swoon over Spongebob, complete with heart bubbles.
In "Stuck in the Wringer" after Spongebob accidentally hurts Squidward, who's writhing on the floor in pain, Spongebob desperately climbs through the passageway between the cashier and the kitchen to see if Squidward's okay. Spongebob slips and lands on Squidward, complete with a SQUISHING sound effect! Then Spongebob tenderly asks him "Are you okay?"
Well of course he'd ask him that in this manner. He's Spongebob!
Near the end of Spongebob, You're Fired, when Spongebob cleans up the mess Mr. Krabs made from trying to cook Krabby Patties at the Krusty Krabs, he puts Squidward in a pink dress.
"Love that Squid" challenges "Rock-A-Bye Bivalve" for the title "Gayest Episode". Squidward is going on a [straight] date, and to practice, Spongebob crossdresses, embraces Squidward, and suggests the possibility of a second date. The subtext is all there, out in the open!