A young Taiwanese assassin codenamed "Glass Heart" committed suicide by jumping off a building, and her heart was pierced by a metal fence. Miraculously, her life was saved by heart transplantation. During her recovery she began to experience strange dreams, which led her to Japan looking for the donor of her heart, who happens to be Kaori Makimura, former partner of City Hunter.
(Source: MU)

[From AnimeNewsNetwork]:

Tending to his sister, who is paralyzed after a fall from a tree, Tatsuya Kitazaki wants revenge. Yet, just as he is about to cut down the tree, a strange and seemingly ageless girl, Sara Nishikujo, appears to stop him. What's more, the girl seems to have the ability to communicate with plants - and she tells Tatsuya the tree's version of his sister's accident. This marks a watershed in Tatsuya's life, as everything begins to change.

Ryo Saeba is a "sweeper" in the city of Tokyo. His works as a trouble shooter, cleaning the streets of vermin, and helping out desperate people. Sometimes he's a bodyguard, sometimes he's an assassin, whatever Ryo does he does it well. In fact his only flaw is his hormones - he loves the ladies and sometimes turns into an idiot when he's near them. Thankfully he's got people like his partner Kaori Makimura to keep him in check.

(Source: ANN)

Collection of Short Stories:
One story is about a pair of lovers always quarrelling and not admitting that they're suited for each other. But their future daughter comes and helps them realise their love. There are also two early city hunter stories in this book.
1. Tenshi no Okurimono
2. Ore wa Otoko da!
3. Neko-manma okawari
4. City Hunter - XYZ
5. City Hunter - Double Edge

A story about a mysterious girl who doesn't seem to age and the people she affects. Very earth-friendly.

From here:
Just before entering university, Yanagiba Masahiko's father died in a car accident. His mother died when he was two, which makes him now really an orphan. But even before the death of his father he didn't have a family life, his father being busy or abroad.

When his mother's younger brother and his wife decide to invite him to live with their family, his life takes a turn. But it is not going to be the normal family life he is imagining himself. What is the "terrible" secret that lead his parents to break the bonds with his aunt and uncle? What could be the true nature of his cousin, Shion? And last but not least, will this "terrible" secret eventually get Yanagiba too?

Yuki Asaka is doctor. This last is received by the grandmother, also doctor to retire. Yuki will cross on his road a friend of childhood, Tatsumi, become as for him honorable one police...

The protagonists of the series are the three Kisugi sisters—Hitomi, Rui and Ai—who run a café called Cat's Eye. The sisters lead a double life as a trio of highly skilled art thieves, leaving cards with the name "Cat's Eye" at the scene of their crimes. They steal works of art (mostly paintings) that belonged to their long-missing father, Heinz (who was a famous art collector during the Nazi regime), in the hopes of him contacting them. Toshio, the police officer investigating this case is the fiancé of Hitomi. He also swears to capture and bring down the Cat's Eye Gang.