Gintoki and Hijikata fighting it out in a sauna with little towels covering their bits. And in another episode, they're handcuffed together. The show even lampshades the whole thing with Gintoki holding up a comic featuring the two of them in a very suggestive pose.
Said comic covers can be found in episodes 92 and 145.
Gintoki and Katsura bicker to no end and know the best ways to push each other's buttons, and yet have shown that they can completely and unequivocally trust and depend on each other when it matters most (see the Benizakura arc and pretty much any time they end up seriously fighting together), suggesting that a much deeper bond exists between them below the surface of insults and mutual annoyance. That, combined with the fact that they're childhood friends who share a dark history of fighting in the war together, leaves plenty of room for speculation.
This sort of thing is really par for the course for a JUMP comic. Early on Gin is willing to fight a giant tentacle monster while armed with nothing but a wooden sword, even knowing that it might cause an interplanetary war if he succeeds, just because Shinpachi is in danger. He also spies on Shinpachi during a date in what even other characters note is just plain weird behaviour. Shinpachi is always going on about how Gin's "samurai soul" is so beautiful and shiny and awesomes, and is regularly seen in a stereotypical housewife outfit cleaning up Gin's apartment for no real reason. Also, after threatening to leave Yorozuya in the Umibouzu arc, Shinpachi (blushing and visibly having been crying) mumbles that he's going to stay with Gin, and promptly scurries off in embarrassment. The whole scene gives off the vibe of a young married couple making up after a spat.
Additionally, in episode 126, Gintoki draws the wrong conclusion from Shinpachi "staying up late and leaving lots of crumpled tissues around." He tells Otae he'll take care of it, and hires some "pretty women" to help Shinpachi. They leave a toy behind after they're dismissed, and Gintoki asks Shinpachi if he wants to use it. Later that same episode, Otae pops in to tell Shinpachi she'll always love him no matter what, and leaves some lotion. Keep in mind Gintoki and Shinpachi were the only two people in the room...
Okita explicitly says that both he and Hijikata are in the Shinsengumi because they love Kondo. This might be in the friendly, platonic sense, but Okita regularly tries to murder anyone he perceives as too close to Kondo, or generally in his way to "Kondo's side". He has an angry rant in one volume that ends with "Hijikata always steals what's precious to me", with a picture of his sister and Kondo. Now read about wakashuu...
There's also a bit in one chapter of the manga where Okita has a meltdown on a rollercoaster, and begs Hijikata to hold him because he's so scared.
Amnesiac Kondo and Katsura become super best pals during a group date, and spend the entire time talking to each other. And singing to each other. The doujinshi artists had a lot of fun with that chapter.
Some of Takasugi's troops are...exceptionally dedicated to him. The most obvious would probably be Nizou, who claims that he follows Takasugi because his presence is like an immensely beautiful, colourful light in the midst of a dark void.
In episode 21, Gintoki grabbed a guy's crotch & held onto it for awhile. Considering what he was dressed like, you could say he was trying to Kappa feel.
Every so many episodes, a man gets something shoved up his rectum (running gag). The situation is most often Gintoki ramming his wooden sword up a guy's butt.
After a night of drunkenness in episode 239 , Gintoki discovers he's slept with six women and...Hasegawa (Madao). It turns out to be one huge prank to get Gin to quit drinking. The twist at the end of episode 240 is that Hasegawa was the only one who wasn't in on it. Yes, Gintoki/Hasegawa may have actually taken place in canon.
For Les Yay there is Otae and Kyuubei, who have become something of a Fan-Preferred Couple to the animators of the anime, who have put the two in every Open and always in some way that makes them look like a couple. They share the honor of being the only pairing to have kissed, though it was forced. It is also the least unrequited of a series Infamous for Unrequited Love, as both characters enjoy hanging out with each other to the point that it's rare to see one without the other.
That said there is also a lot of angst on Kyuubei's part as she is in love with Otae but believes Incompatible Orientation is in effect, so her strongest wish is to be a guy but she also seems to like being a girl. Otae is just a complete mystery orientation wise or what her feeling toward Kyuubei are. This all becomes a plot point to the Gender Swap arc, that by the end is still unresolved.