In Fruits Basket, Haru often hits on Yuki, usually while in "Black" mode.
Not to mention Haru tells Tohru that Yuki is his "first love", and Yuki implicitly supports this by warning Haru not to mention it again.
Shigure and Ayame intentionally start up suggestive conversations nearly every time they meet, as part of some sort of Running Gag between the two.
Shigure and Akito had loads of suggestive scences together until Akito was revealed to be a woman..
Then there's that one scene where Kyou wakes up to find Ayame sleeping next to him in bed. He goes into a shocked state and Ayame mumbles "I'm still sleepy", grabs Kyou and tries to cuddle with him. We then see him covered in bandages from after Kyou beat the crap out of him and Ayame states he snuck into Kyou's room because Yuki had locked him out of his room when Ayame tried to sneak in.
Later Ayame tells a story about how he volunteered to let all the boys at his high school... express their desires with him.
Apparently, when he was Student Council President he claimed that if needed, he'd give himself to both men and women alike.
And then there's the tension between Yuki and Kyou (they're quite a popular Slash Fic pairing as well), best shown when they fight and Yuki got close enough to kiss Kyou before kicking him away. And then there's Tohru's "what would happen if Kyo and Yuki got along" fantasy with a lot of Bishie Sparkle. Also Shigure once said that Kyou and Yuki's arguing makes them sound Like an Old Married Couple.
In the English dub of the anime Kyo and Yuki start almost all of their fights by shouting let's do it! and clenching the fronts of each others' shirts. Kyo and Haru do this once in episode 10 as well. One of their first fights begins with Yuki saying he's going to give Kyo exactly what he wants and that he's not going to hold back ... right before undoing a couple of his shirt buttons.
Kyo's *ahem* obsession with Yuki is typically hostile, but he expresses blatant worry at times when Yuki is vulnerable. When Yuki collapses from an asthma attack Kyo abates his fight with Haru to see if he's ok, and when Yuki is confronted by Akito Kyo can be seen watching from afar with a frown on his face. This shows that while Kyo's resentment and jealousy drive their relationship, he does care for Yuki's well-being deep down, or at least does not want to see Yuki hurt by anyone other than himself.
Takei Makoto the Student Council president at Yuki and Tohru's school is shown to have a crush on Yuki, blushing whenever he is around and imagining him wearing a girl's uniform (skirt included) with a smile on his face.
To convince Takei that his hair is naturally black and white, Haru drags him into a closet and presumably shows him his pubic hair.
Ayame has a great admiration for Hatori and only listens to him because of it.
Also, in regards to the girls Hanajima Saki's and Arisa Uotani's and affections for and devotion to Tohru seem to go much deeper than simple sisterly friendship. They constantly protect her and threaten people that bother her.
In episode 10 Hana collapses during an endurance run and Tohru expresses blatant worry and comes to her aid and they both hold hands while looking into each other's eyes.
The manga hints a little more strongly that Saki in particular is suppressing deeper feelings for Tohru. During the play where she's cast as Cinderella, instead of mooning over the prince (Yuki,) it's Tohru she obsesses over and gets rather possessive about. Near the end, when she finds out Kyo is taking Tohru away, she gets very quiet and pensive, with her brother giving her an understanding look and asking if she's ok.
Kyo mentions worrying about losing Tohru to Rin, and this Troper thinks he has reason to worry. For example, Rin evidences conflicted emotions regarding Tohru. She rejects and harbours resentment towards what she sees as Tohru's interference in the family; Tohru is an outsider and she cannot understand. However, internal dialogue reveals that as early as their first meeting Rin is also possessed by the same desire that many of the Jyuunishi develop; to fall into Tohru's arms and be comforted. Her view of Tohru as a maternal figure manifests to the extent that on the verge of fainting she mistakes Tohru for her mother and responds with utter terror, cowering and pleading for forgiveness before she loses consciousness. Eventually Rin's physical distress, despair and torment culminate in her breaking down sobbing in Tohru's embrace. Though she never evidences such extreme vulnerability again, her previously aggressive behaviour softens and it is clear she cares for Tohru deeply. Kazuma commented that Tohru became Rin's first friend, being the first one outside of the Sohma house to become worried about her.
See also: Tohru's reaction after seeing Rin naked (post-transformation).
Akito is worthy competition as well seeing as how even though it might be an act in the manga where Akito is female she acts really affectionate with Tohru and they eventually become close friends.
Tohru and Kisa. Tohru is Kisa's make-believe 'Onee-chan' which means 'big sister'. On the day she met Tohru, she bit her. But after running out of Shigure's house, Tohru finds Kisa and makes a very inspirational speech. After that, Kisa clings to Tohru like a real little sister does to her big sister. She always sees Tohru as her big sister and in the anime, she always calls her 'sissy'. Kisa loves Tohru very much, and goes on and on about her. She tells Hiro that whenever she's around Tohru, she feels all warm inside. Hiro says he doesn't like Tohru at all due to jealousy and Kisa is very sad and surprised at his reaction to Tohru.
After Tohru's initial encounter with Kisa the latter follows the former around for the duration of her stay. While Kyo cracks that it would bug the crap out of him, after Tohru stops walking and Kisa bumps into her, Tohru squeals and glomps her. After Kisa leaves, Tohru mentions her slight sadness at not having her around. Later volumes of manga have scenes where other characters are talking and the reader can see little hearts floating into the more serious panels, revealed to be emanating from Tohru and Kisa hugging each other. Every time they see one another, Tohru has the same squeal-and-glomp reaction.
Akito in the anime where's he male instead of female like in the manga where in episode 8 he gets really close to Hatori following inflicting Eye Scream on him trying to make him feel better and asking him what's wrong and later getting really close to him again and caressing his hand up his tie.
When Yuki makes a public reference to the number of times Hatori (the Sohma family doctor) has seen him naked, the girls listening are seemingly horrified... and simultaneously strangely fascinated.
Akito and Yuki in the anime where Akito is male, not in the manga where Akito is female have a very messed up relationship that can be seen as a twisted form of this, as shown when Akito gets close to Yuki and caresses his face with his hand but Tohru picks up a threatening atmosphere about him and pushes him away from Yuki.
Haru is very enthusiastic about allowing Momiji to wear a girl's uniform to school.
And all of the students, boys and girls, were overjoyed to see Yuki cross-dress.
Towards the end of the manga, after a ton of back story and character development, it's revealed in a huge fight that Yuki and Kyo both really admire each other and always have (Kyo for Yuki because of how perfect Yuki wanted he is in the family, Yuki for Kyo because people outside and inside the family gravitate to Kyo and always want to be friends with him). Yuki explicitly says to Kakeru that all he wanted was to be friends with Kyo when they were younger, but Kyo already hated him (see the hat incident). While their frustrations stem from mutual dislike built on a lot of pain, it also stems from envy, and they eventually do become friends by the end of the book.