Hi everyone! I've been into K-dramas and J-dramas for a while, but I stopped watching a lot of Japanese media because they always seemed to center around students. I would like to watch some Japanese dramas and movies that aren't about high school romance or teenage angst.

Dramas I've seen and enjoyed: Kimi wa Petto (original with MatsuJun), Ouroboros, Densha Otoko, SHINSENGUMI!, Saiyuuki. I also enjoyed Hana Yori Dango, Nodame Cantabile, and Honey and Clover but I'd like to stick with things about adults with jobs. Bonus points if they feature adult women who aren't mothers.

Thanks in advance!

Nigeru wa Haji da ga Yaku ni Tatsu, Mondai no Aru Restaurant, Dear Sister, Saikou no Rikon (married women but not mothers), Love Shuffle, Love Song, and Long Vacation. The following are if you don't mind episodic dramas: Okitegami Kyoko no Biboroku, Kounodori, Juhan Shuttai!, Galileo, Keizoku 2: SPEC, and 37.5°C no Namida. :)
If you're looking for jdramas with adults who have jobs and some romance then I'd rec:

Please love the useless me
Nagareboshi
Rich Man Poor Woman
Hotaru no Hikari
Love Shuffle 

- Yae no Sakura (period drama like Shinsengumi, and it follows the main character's life since she was a little girl, but most of the drama shows her life as an adult)
- Ghostwriter (a thriller about an author and her talented ghost)
- Kazoku no Katachi (comedy drama; it's light on romance and more about making connection with people)
- Saigo Kara Nibanme no Koi (slice of life; the female lead is forty something, I think, who never married and never had a kid)
- Haken no Hinkaku (comedy workplace drama with a little sprinkling of romance)
- Arifureta Kiseki (slice of life; had an undertone of sadness at first but gradually became life-affirming)
- Biblia Koshodou no Jiken Techou (bookstore worker who solved mysteries using her knowledge of books; and it really is more interesting than how I made it sound)

None of the female leads in those dramas are mothers. Hope that helps :)
Hi Melissa!
There are quite a lot of jdramas for adults, but I will try to make a short list based on recent dramas (2017-2016).

Quartet (airing) : the story revolves around 4 adults, two men and two women, who formed a quartet and live together in the prefecture of Nagano. They all have their secrets, and all struggle with their life. It's really well done!

Juhan Shuttai! : a young girl is hired in a publishing company and is affected to the manga department. She's full of energy, and does her best in a world where people don't read as much as before. No romance here, but a great story about work.

Boku no yabai tsumai : a woman is faking her own abduction and starts to make her cheatting husband's life a hell. It's full of suspense, you can't predict what will happen. If you like the genre, don't miss it!

Love Song: a former musician refuses to work in this field again because of a painful experience. But one day, he meets a very talented young girl with an enchanting voice. But this girl has a stutter and because of that, it's difficult for her to communicate with others. In this drama, the second leads were really good!

Alos, I had a look at your drama list, and I saw that you planned to watch Last Cinderella. It's a really good drama, and you should give a try.
There are so many dramas about adults, I rarely watch school dramas. I really agree about the above mentioned Saigo Kara Nibanme no Koi, it's so funny and hearwarming. Here are a few more that I recommend, there are many more of course

Hirugao (romance: unhappily married women happen to meet people they fall in love with)

Ice World (detective/romance: a man meets a woman accused of murder and tries to find out the truth)

Itoshi kimi e (romance: female doctor meets photographer with a disease)

Long Goodbye (detective, great story)

Manhattan Love Story (comedy: people who come and go at a coffee shop where stuff just happens...)

Bara no nai hanaya (romance: single dad who owns a flower shop meets bilnd woman, secrets and lies)

Roosevelt Game (business/sport: the company is about to go down but the baseball club can save the day THIS DRAMA IS AWESOME)

Chase (crime/detective: it's an awesome hunter/hunted story about a criminal and the guy who tries to catch him)

Shinya shokudo (food/slice of life: a restaurant that opens at midnight, it's about the owner and the people who eat there, each episode has a different story and a different dish)

Date (romance/comedy: two adults who aren't like everybody else are, for different reasons, thinking about getting married)

Dinner (food/slice of life: an a very skilled chef tries to help a restaurant that isn't going so well to survive)

Underwear/aka Atelier (slice of life: a young woman comes to work for a famous underwear designer and learns about her goals in life)

Virgin Road (romance: pregnant woman finds a guy to act as her fiancé while she goes to visit her father)

Gunshi Kanbei (historical: the life of the brilliant strategist Kuroda Kanbei and the lives of those around him, AMAZING drama)
Okay everyone here has made pretty reasonable recommendations.I only have one.
'Saikou no rikon' - 'The Great Divorce' 
A hilarious 'adult' drama 
Information link : http://mydramalist.com/5992-saikou-no-rikon
Sources : http://kissasian.com/Drama/Saikou-no-Rikon
 https://www.amazon.com/Divorce-Japanese-English-Di...
Here is a synopsis
 A romantic home comedy about 30-year-olds with an immature view on marriage that focuses on themes related to married couples and families in general. The protagonists of ‘Saikou no Rikon’ are two couples – Mitsuo and Yuka as well as Ryo and Akari. Mitsuo and Yuka have been married for two years, but their ways of thinking and living are completely different and they keep on quarreling with each other most of the time. Kosei is already regretting his marriage every day, yet his grandmother finally wants to see a great-grandchild. One day, he happens to meet Akari, his old girlfriend from his student days, which brings back pleasant memories. Right after he finds out Akari is already married, Yuka eventually asks him for a divorce but Mitsuo still ends up living with Yuka under the same roof due to some reason
Of the comedy,Slice of life and romance genre. I hope this is what you are looking for, when i was in japan a few years back for me this was a hidden gem among stones , although it started out slow i really enjoyed it , if you decide to watch it i hope you enjoy it too.
- Ak
Pride
It's not that I can not marry but I don't want to
Maou
Nagareboshi
Hotaru no Hikari
We married as a job
Cheap love
Buzzer Beat
Love Shuffle
The quiz show
Liar game
Please love the useless me
Suzuki Sensei is a school drama told with an adult narrative.
Soratobu Kouhoushitsu is about adults with jobs with a little bit of romance.
Summer Nude (2013) Yamashita Tomohisa. Karina. Toda Erika 
Watashi ga Renai Dekinai Riyuu (2011) Karina
Kekkon Shinai (2012) Tamaki Hiroshi
Kyou wa Kaisha Yasumimasu (2014) Ayase Haruka. Tamaki Hiroshi 
Kaitou Tantei Yamaneko (2016) Kamenashi Kazuya. Narimiya Hiroki
Kurosagi (2007) Yamashita Tomohisa. Horikita Maki. 
Orange Days (2004) Shibasaki Kou. Narimiya Hiroki. Eita. 

Dramas I Second: 
Hotaru no Hikari 
Rich Man, Poor Man 
Love Shuffle 
Please Love the Useless Me 
I would recommend these:
1. Sapuri
2. Last Cinderella
3. JIN (historical)
4. Majo no Jouken (the male lead is a high school student though)
5. Kaitou Tantei Yamaneko
6. It's Not That I Can't Marry, But I Don't Want
7. Hotaru no Hikari
8. Doctors’ Affairs
9. Around 40
10. Anego
11. A Girl & Three Sweethearts
12. Nobunaga Concerto (historical)
13. Watashi wo Hanasanaide
(I first saw the english version of this drama––based on the Japanese novel––"Never Let Me Go".)

PS! I have a thing for an older women and a younger male, it this isn't your cup of tea, then skip: Sapuri, Majo no Jouken, Anego, A Girl & Three Sweethearts (the gap in age doesn't effect the storyline), It's Not That I Can't Marry, But I Don't Want and Last Cinderella. All dramas in which the age gap is a part of, or an issue the drama deals with.