I've watched a lot of jdrama in my life so I'll try to put a few with differents genres. My favorite are definitely the one written by Sakamoto Yuji but since i don't know what you like i thought it'd be best to put other kind of dramas:
- Kisarazu Cat's eye (comedy/friendship)
- Woman (slice of life/family)
- Kazoku Game (psychological/family)
- 3 nen B gumi Kinpachi sensei season 7 (school/drama)
- Legal High (law/comedy)
- Soredemo ikite yuku (slice of life)
- Nodame cantabile (classic dorama/music/comedy)
- Nigeru wa haji da ga yaku ni tatsu (romance/comedy)
- Orange Days (friendship/romance)
- Ryusei no kizuna (mystery/comedy/family)
- Switched (school/supernatural)
- Aishiteru (drama/family)
- Kahogo no kahoko (family/comedy)
- Saikou no rikon (divorce/comedy)
- Yume no california (friendship/drama/life)