Here are my favorites from the late 90s through 2010.
Cheap Love: A romance between a teacher and a nightclub worker. Excellent story with a terrible last episode/ending but it's still worth the watch. I just pretend the last episode didn't happen. XD
Home Drama: A show about a found family brought together by a tragic accident while on holiday.
Kimi no Te ga Sasayaite Iru: A short drama about a blind woman's life.
Majo no Jouken: Forbidden romance between a teacher and a student.
The Rose: One of my guilty pleasure shows. Essentially a soap opera about a young woman moving in and interacting with her newly found mother and her half siblings.
Ryusei no Kizuna: Three siblings plot their revenge on the person who murdered their parents when they were children.
Snow White: A young woman has a chance encounter with a young man in Japan who turns out to be her best friend's brother. The pair end up living together out of the young woman's love for his brother and hijinks ensue. This is an underrated shows on Mydramalist.
Sora Kara Furu Ichioku no Hoshi: I see this is on your plan to watch. This was an enjoyable thriller with a unique story about the relationships between a detective investigating a murder, the detective's sister, and the murder suspect. Be prepared for a shocker of an ending!
Three Dads One Mom: A young woman has fertility issues and her husband's friends offer to help. She loses her husband and gives birth to a daughter without knowing who the father is. Cue three men and one woman trying to raise a baby together.