1. Kohrogi
Mitsurugi Kai is a wizard that must pass a test of character. He doubts himself due to his past. His test is to retrieve paper charms by himself. On his way, he meets Kohrogi Orine, a fledging singer who also doubts herself.
2. NOIZ
Hayami Shrou can see into the future of people by touching them. Two years ago he lost his parents in an accident, while his sister barely survived, but remains unconscious. He blames himself, for, if he had touched them and saw into their future, he could have saved them.
3. dZi:s
4. X-connection2001
(Source: MangaUpdates)

Whistle! is about a boy named Shō Kazamatsuri. He transfers from Musashinomori School to Sakura Josui Junior High School for better hopes to make the soccer team, since he never got a game at his old school due to his small stature. Yūko Katori, his teacher, introduces him as a former star of the famed Musashinomori team, causing his classmates to be wrongly ecstatic. Right after that, one of the players, Tatsuya Mizuno, reveals that he was never a regular. In other words, since he never got the chance to play, Shō is a poor player. Shō struggles to improve his skill so he can make the team at his new school and to ignore the drastic disadvantage he has due to his height.

From Doko Demo Doa Manga Scanlations:

Yuika Aoi has a recurring nightmare in which she isn’t able to save a mysterious, green-eyed man called Rei. Her elderly grandmother, who was born in the Taisho era, lives very traditionally, and at times seems to have magical powers. Apart from all this, she is a normal high school girl until she falls off a roof and into the Taisho era, in the middle of a battle between Rei and a fairy. Will she be able to save him this time?

Hayami Shrou can see into the future of people by touching them. Two years ago he lost his parents in an accident, while his sister barely survived, but remains unconscious. He blames himself, for, if he had touched them and saw into their future, he could have saved them.

Six years ago, Kasumi Shirou was the sole survivor of a plane crash. Though he lost normal vision in his right eye as a result, he gained the power to see into the past. Now a high school student, Shirou is bent on using his abilities to track down the man who murdered his mother.

Hungry for a teacher and student relationship? Nope, it’s not about love or romance. It’s all about sport! Find out what happens if both the teacher and student, who have nothing in common and hate each other in the beginning, are connected with hockey as their life.
(Source: Doko Demo Doa Manga Scanlations)
Includes the one-shot Kami no Bannin.