Please recommend any romantic manga, that is not corny and plain, but one that is exciting, romantic and unique.
Akagami no shirayuki-hime, Horimiya and Akatsuki no Yona. I don't read romantic things but they are probably the only thing that I like in the romantic genre.
Seconding Akagami & Akatsuki no Yona, far has great taste there. If you ever feel like crying (well, I cried too much that I had to stop reading ;w;) I recommend Immortal Rain, but it is a bit cheesy. The storyline is definitely unique imo.
Also, not very romantic yet, but I'd also mention Song of the Long March since it looks like it'll be more romantic as more chapters are released. One of my favorite fantasy series is Mahoutsukai no Yome. You COULD consider it a romantic series but I believe the author wants us readers to think differently for now (if you catch up with the latest chapter, you'll know what I mean). Definitely VERY unique. (Not very romantic though, but exciting and interesting xD)
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"My Love Story!!" It's so sweet and avoids so many of the cliches in romance manga, it's one of my favourites!
Also, my absolute favourite manga ever: Victorian Romance Emma! (Also known as just "Emma" sometimes.) It's so so so gorgeous, it's set in Victorian London and it's a love story between a maid and a rich man and it's so beautiful and well-written and well-drawn, I cannot recommend it highly enough!
Mahoutsuki no Yome/Ancient Magus' Bride is amazing, yes, I second this recommendation! There are hints of romance, which keep us wanting more, plus the story is fantastic!
Let's see...
[URL=https://myanimelist.net/manga/32137]3-Level Combination[/URL] - a romantic/seinen/comedy/drama manhwa (with gorgeous art!) that not many people know of but I think is a hidden gem. [URL=https://myanimelist.net/manga/655]Please Save My Earth[/URL] - starts as a boring one (imho) but develops into an unbelievable sci-fi story with romance as one of the main plot points. I was pleasantly suprised, just needed to give it some time to develop.
HoneyBelle beat me to "My love story" XD So I second that recommendation.
In terms of unique Tokyo Crazy Paradise fits the description pretty well. It's more action focused, with romance and comedy as well :D
Crimson Spell is really good!! It's yaoi and has an interesting plot.
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My favorite one is Lovely Complex if you haven't read it ~ ^_^
I also really liked Hana no Namae, but it's kinda dark...also it's either a hit or miss. I've enjoyed it every time I've read it though.

Oh gosh yes. XD Very good series. But yes, yaoi meaning more explicit (In case OP isn't comfortable with that stuff)
Peach Girl is pretty old now that I think about it, but it's a great anime full of drama and intense romantic scenes. And by drama, I mean there's so much shit going down it's silly and definitely a good dose of "Aww's" and "WTH IS HAPPENING AHHHHH's"!
The only romance manga that I remember reading is Say I Love You. I thought that it was a pretty solid one, so I would definitely recommend it!
In term of anime, Yuri!!! on Ice has a pretty solid romance side-plot...
Here's a list of some that I've really enjoyed in the past and so far. Hope you find them interesting!
Tomo-chan wa Onnanoko!(incomplete) Tomo Aizawa was able to successfully confess to her crush Junichirou Kubota. There is only one problem: He just sees her as his buddy. He even thought that she was a boy until they went to middle school together, because her grade school was in a different school district. So, Tomo-chan's struggle for Jun's affection begins.
Fruits Basket(complete) Tohru Honda has been living in a tent since her mother dies in a car accident, but ends up living instead with Yuki Sohma, her school's "prince", along with his relatives Shigure and Kyo. But Tohru soon discovers that the Sohma clan has a secret of it's own: certain members of the family are possessed by the animals of the Zodiac, so whenever they are hugged by a member of the opposite sex they turn into that animal! Tohru promises to keep their secret and vows to somehow break the curse, and she may just end up healing the Sohma clan members in other ways as well...
Cat Street(complete) he story centers around Keito Aoyama, a former famous child actress. Due to a childhood incident, she retired from her career early and withdrew from normal society. Now 16, she passes her days in boredom and without purpose. But one day she runs into a stranger who takes her to El Liston--a free school for high school students like herself, who don't have a place where they belong. Though hesitant at first, Keito decides to enter El Liston and subsequently, she begins a new stage in her life.
D.N.Angle(incomplete) Daisuke Niwa is an ordinary, if slightly unlucky, middle school student. On his fourteenth birthday, he comes down with a 'condition' that has plagued the men in his family for three hundred years. When he sees his crush, Risa, he transforms into his alter ego, the phantom thief Dark Mousy. Unfortunately, when Dark Mousy sees his crush, Risa's twin Riku, he transforms back into Daisuke. The only cure for this craziness is if Daisuke can get Risa to fall in love with him ...
Midnight Secretary(complete) Kaya Satozuka is a brilliant secretary who excels at her job, which is why she doesn't bat an eye when she's assigned to be personal secretary to Kyohei Touma, the very difficult managing director of Touma Foods. It doesn't faze her when her new boss seems determined to make her fail, and she even manages to take it in stride when she discovers the secret behind his prickly behavior…he's a vampire! But while Kaya easily adapts to late nights and keeping a schedule of his "dinner dates", will her ultra-competence help when Kyohei's smoldering gaze starts turning her way?!
Basara(complete) "Basara - The spirit of freedom which denies old authority, transcending traditions and customs." Born under a prophecy that will liberate and unite Japan, Sarasa has had to take her brother Tatara's place as the "Boy of Destiny." Fighting for the oppressed, Sarasa journeys across Japan to gain allies and defeat her enemies--all while keeping her identity a secret!
Biyaku Café(complete) The aphrodisiac night retreat is a place with no menu, and the tea is made to the customer's image by the employees. An omnibus story surrounds the overbearing masters, various customers, and the tea!