Despite the conflict, there is an attraction. This is obvious to everyone except the couple. Confront them with the obvious, they'll deny it. When one gets clued in, they will do every thing in their power to play it off. The other soon does the same. Sometimes they will progress to admitting their friendship but insist they are Just Friends.
Might involve a Can't Stand Them, Can't Live Without Them situation, or even Domestic Abuse (but usually Played for Laughs). Expect frequent cases of Rescue Romance, even before they are officially a couple.
If there is a Love Epiphany with one of these characters, expect it to change nothing, at least in the short term.
Many subsequent anime and manga creators have followed in her footsteps, especially after the popularity of Ranma ½.
All examples (with the exception of Takahashi's own works) should be placed in Belligerent Sexual Tension.
Female Lead: Lum Invader, a "more dere then tsun" type of Tsundere. A beautiful teenage alien from the planet Oniboshi, who, due to a misunderstanding thought she and Ataru were married. She is lovely most of the time, but not afraid to shock her 'Darling' if he acts out of line by hitting on other girls.
Will They or Won't They? is somewhat resolved, in the sense that it is made clear that they are the Official Couple, even if they aren't offically together. By the end it is clear that Ataru does love Lum ("I'll never forget you Lum!"), and that she is well aware of this fact, but he still Cannot Spit It Out, due to his perverted personality and fearing the wrath of his classmates.
Interestingly, originally Shinobu Miyake was supposed to be Ataru's Love Interest, but Takahashi was forced to retool due to Lum's popularity. This is clear in the early chapters where Lum is more of a Temporary Love Interest, but by a few volumes in, Lum has been promoted to female lead and Shinobu demoted to major side character (she had major Ship Tease with Shutaro Mendou and is eventually put in a Beta Couple with Inaba).
Male Lead: Yuusaku Godai, is an Unlucky Everydude, usually a nice guy, to the point where he doesn't fit the Jerk with a Heart of Gold stereotype so much as he's a lazy, cowardly, wishy-washy person who's rather immature and unable to say "no" to anybody, be it an unwanted girlfriend or a drunken flat-mate, although he is a bit of a Covert Pervert, and often offends people with his attempts to please everyone. His progression from loser trying to get into college to responsible adult is one of the primary Character Development aspects of the work. Much less of a jerk than other characters in Takahashi's work. Notably, his rival fits this mold a little better (as a good-hearted but very conceited rich boy) and has similar character development.
Will They or Won't They? is finally resolved after 70 plus episodes. Ending on a definite note with Godai and Kyoko married and with a daughter named Haruka. Their issues were more serious and realistic (Godai's wishy-washiness, Kyoko's inability to let go of her late husband) than Takahashi's usual stubborn Will Not Spit It Out.
Ranma: Jerk with a Heart of Gold, probably due to his experiences growing up. Raised as a super-ultra-macho fighter by his Jerkass father Genma, who put him in an Arranged Marriage with one of Soun Tendou's daughters - the one who's ultimately "chosen" is Akane.
Akane: Tsundere. Varies; the manga makes her more deredere, the anime gives her more tsuntsun aspects than she had in the manga but she can still be considered more deredere. Due to the death of her mother very early in her life, Akane badly wishes to be more feminine, but as the only Tendo girl with martial arts skill her father raised her as a Tomboy.
Ranma seems to be locked in a similar situation with all his possible Love Interests. Shampoo loves him but she can also be very violent and possessive as well as prone to attacking those who get in between them once in a while, whereas Ukyo has Childhood Friends deets but she also can get snippy to him (and both have been argued to have more than one whiff of Yandere), and Kodachi is... well, herself.
Many a fan theory exists as to why they're so unable or unwilling to admit the obvious: a combination of Ranma's ultra-macho upbringing and Akane's Kuno-induced misandry being the most popular. Plus, they are still in high school so perhaps a lack of progress is understandable. At least some (minor) hints of progress at the very end - they hold hands. Ranma confesses he loves Akane, although he denies it later.
InuYasha: Jerk with a Heart of Gold. Half-Human Hybrid born from the union between a human noblewoman named Izayoi and a powerful dog Youkai only known as the Inu-No-Taishou ("leader of the dogs"). Raised in a rich human household, where people looked down on him for his origins. Lost his mother early in his life, then some years later he met a lonely Miko named Kikyou who offered him kindness, and they fell in love due to their common issues. They were planning to use the Shikon no Tama to make him a fullblooded human so he could live with Kikyou happily, but then... Naraku happened. Kikyou died, Inuyasha ended up pinned to a tree for 50 years until Kagome released him - logically, he has huge issues in regards to people.
Kagome Higurashi: Tsundere, but more deredere then tsuntsun. Kikyou's reincarnation, a middle school student who lives in modern Japan. Is accidentally thrust into the past and, to protect herself and her surroundings, releases Inuyasha, and later teams up with him to retrieve the lost Shikon shards. Has a good heart, but latent self-esteem issues as well as quite the uncertainty in regards to her own place in the world - none of which is helped by the fact that, later, the original Kikyou is forcibly revived, dredging up Inuyasha's complex feelings for her and leaving Kagome both insecure about her own worth as a person, and wondering if she's necessary at all for him.
Inuyasha and Kagome are a variant: They clearly have come to an understanding as to their mutual feelings, so tend to have moments of Aw, Look! They Really Do Love Each Other occasionally sprinkled into the denials, fighting, and plot-stretching bouts of Cannot Spit It Out. They actually do become an Official Couple towards the end of the manga (and appropriately enough, their romance then receives much less attention until the end). Not to mention, thanks to Character Development, Kagome warms up to Inuyasha quite faster than the standard Takahashi Tsundere, and Inuyasha is slightly less prone to verbal abuse than the standard Takahashi Jerk with a Heart of Gold. A far more standard example within the series would be the secondary couple, Miroku and Sango, although Miroku is less Jerk with a Heart of Gold and more Handsome Lech, with his incessant flirting with every girl the group meets being the primary trigger for the tsuntsun outbursts of Sango, who's normally a Yamato Nadeshiko unless she's dealing with him.