In the Yu-Gi-Oh! manga, there is definitely some questionable statements Jounouchi makes to Yuugi. One humorous lampshade example being when Yuugi mentions that their digital pets have the ablity to mate and gain strength from each other (which is awkward in the first place) to which Jounouchi responds, "Yuugi and I must mate at once!" Honda comments in frustration that people overhearing might get the wrong idea.
The Toei anime has several easter eggs of this nature involving Yugi and Jounouchi. One episode shows them during judo. They're both wearing white martial arts robes. At one point, for a very short time, they end up in this◊ position. In a much later episode, they're walking towards the gym from the pool, wearing towels, and Yugi comments 'that felt good'. There's no way that wasn't intentional Ship Tease.
It's not just Yugi and Jounouchi...there's a point in the Toei anime where it looks like Yami is hugging Yugi's soul.
Yuugi and his "Other me"/Yami, Atem. Suffice to say "soul mates" might actually be a good way to describe their relation to one another.
Oh dear god. Where to even begin with those two? Hmm, maybe the hand-holding that happens at least three different times throughout the series? Or the fact that Atem likes to cradle Yugi in his arms whenever he gets hurt? Or the only time the big bad Pharaoh ever cries is when Yugi gets his soul stolen? Or just the general overprotectiveness going on from him? Or maybe how Yugi makes multiple speeches about how sad he's going to be when Yami has to leave him, often ending with tears?
And then there was that time Yugi almost burned to death while assembling the Puzzle so that he could see Yami one last time. Plus Yami does tell Yugi he wants to be with him forever...and Yugi offers him all his memories in exchange. Yami repeats the sentiment...while on a date with Anzu.
Let's not forget in the Yami vs. Weevil duel during the Doma arc. Yugi's soul has been stolen, and Weevil claims to have his soul card. He rips it in front of Yami's eyes... then taunts him by revealing it was a joke. Yami goes berserk and deals enough damage to Weevil that turn to effectively defeat him THREE TIMES over.
They play Those Two Bad Guys throughout the Battle City arc, appear in each other's dreams, Marik ends up in Bakura's body... after which Bakura dies trying to save Marik- Bakura loses his soul, his body, and the Ring in an attempt to protect Marik's soul from being destroyed. Bakura also saves the life of Marik's brother to help Marik, for no benefit to himself. Not to mention all the time they spend staring at each other...and all the sexual tension during the scene where they first meet. And the fact that they agree to be partners when they first meet, even though neither of them had ever worked with anyone as an equal before that. And the way they compliment each other, though neither of them is prone to give compliments to any other character in the series...
Also comes up between Jounouchi and Kaiba. Kaiba refuses to acknowledge Joey as a duelist, Joey blusters at him, Kaiba insults and ignores him, and Joey has potentially homoerotic dreams about being defeated by him. Certain parts of fandom have fun with that.
Remember that cute scene, when Shizuka/Serenity jumped into the sea to save her big brother? Guess who saves him in the manga? Sadly, not by jumping into the water (he doesn't care that much!), but rather by dropping the key. Still, good enough for any shipper.
They also share a bunch of similarities - they're both an older, protective brother, favour BEWD and REBD, they both had difficult childhoods and they both either are or were huge jerks. They're complete foils to each other, and Jounouchi's the only one who really seems to want to get through to Kaiba for reasons other than his help in saving the world.
In the original Japanese version, after Jounouchi and Kaiba duel at Duelist Kingdom and Jounouchi loses, Kaiba says, "Jounouchi... it really suits you to be on your knees."
Also, Kaiba spent most of Season Zero either spying or stalking Yugi to see if anyone was trying to defeat him in a card game, can't go more than four episodes without sending his top minions to attack Yugi's friends and family in an attempt to defeat him, and spent millions of dollars developing advanced hologram technology and building a sky scraper for the sole purpose of defeating him. And we haven't even gotten to Duel Monsters yet.
Season Zero also has lines like this:
Kaiba: Looks like we really are connected by the thread of destiny. Try to cut it, but it cannot be broken...A thread that entangles us.
And what about when Kaiba is defeated by Dartz? Before he dies because his soul has been stolen, Yami sustains him in his arms, while Seto, with his last strength, asks the other to avenge him.
When Yugi and Kaiba duel at Duelist Kingdom, Kaiba has an internal monologue about how dueling with Yugi makes his heart beat faster. (Or he did in the Japanese version.)
Season Zero has three cases where Anzu is the subject of Les Yay:
There's her regular, close, teasing friendship with Miho.
One episode features a girl who professes a crush to Yugi (she's actually a literal witch out to steal a rare card of his). The point is supposed to be made that Anzu is jealous due to her own feelings for Yugi. But the scenes are played so that Anzu is in constant confusion about "not understanding these feelings", and styled so that she's fixating a lot more on the girl than on Yugi, which makes Anzu come out looking like a closet lesbian/bisexual.
There is some Anzu/Mai (danceshipping) subtext in the manga. Look at this panel from manga chapter 28.◊ Anzu just got through with telling Kaiba off for being a jerk about defeating Jounouchi in a duel and apparently Mai decided that the best thing to do to cheer Anzu up was to randomly stroke her hair.
In a lower level, there're fans who pair Honda with Otogi. It mainly started because of the Foe Yay with Shizuka in the middle, but they ended up spending more time together rather than with her.
In the manga during the Monster World arc, there's some of this between Ryou Bakura and the Spirit of the Millennium Ring (aka Yami Bakura). Basically Yami Bakura stabs Ryou in the chest with the pointy parts of the ring so Ryou can't take it off, then goes on about how Ryou should be his permanent host and talks about how good it feels to be inside of him.
Heck there was also that moment during Battle City when Yami Bakura purposefully allowed himself to be seriously injured during his duel with Yami Yugi and switched consciousness with Ryou Bakura (in the Japanese version, he would have died had the duel continued) in order to make Yami Yugi surrender the duel. Then Yami Bakura, upon seeing a hurt and frightened Bakura plead for his life, switched places with Ryou so that he bore the brunt of the pain from Yami Yugi's attack and allowed his host to survive.