Time Travel, Crime & Supernatural Dramas

I'm looking for something where the character goes back in time not forward. The further back the better, although I don't mind if its only a few years.

I've watched JIN both the Korean and Japanese, Nobunaga Concerto, A Step Into The Past, Faith & Myth.

I'm very picky with my crime dramas so I'll just list the ones I've watched and just recommend similar ones.

I've watched Cruel City, IRIS 1 & 2, Joker Yurusarezaru Sousakan, Missing Noir M, I Remember You, Love Me if You Dare, Sennyuu Tantei Tokage & You're All Surrounded

Also I'm looking for dramas that have supernatural elements, such as, ghosts, vampires/werewolves, even things like reading people's minds.

I've watched Cheo Yong, The Great Seer, My Girlfriend is a Gumiho, Signal, The Master's Sun, Blood, You Who Came from the Stars, Blade Man & I Hear Your Voice.

Sorry for asking for so much, I just figured that I would list them all here instead of making three separate posts. Thanks in advance!

I think you've seen most of them haha. (I recc the same as the previous poster! GG and Nine were great dramas.)
If you end up making a list (according to your taste) of the crime/time travel dramas, I'd really love to see it please!

Ok... I'll only add those you didn't watch and might interest you. But you should update your list, it would be easier for recommendations.

Time-travel dramas :
- Back to 1989 : taïwanese drama, romantic comedy - As the title says, the man goes back to 1989. There, he mets his mother's best friend and later, his mother. He wants to take this opportunity to find out who is his father. Interesting so far, even if just to see how the taïwanese society evolved in 27 years.
- Faith (highly recommended) : kdrama, supernatural, medical and romance - A plastic surgeon is kidnapped by a General who brings her 700 years into the past, thinking she's from heaven. By the way, people have supernatural powers in the past.
- Nine : Nine Times Time-Travel (highly recommended) : kdrama, romance and crime : The man goes back 20 years into the past each time he burns an incense item.
- Operation Proposal : kdrama (Proposal Daisakuken is the japanese version and good too), romance and sports - A man goes to his best-friend's wedding, regretting to have never told her his true feelings. I don't remember how but he gets the chance to go back in time for several occasions in order to try changing his destiny with her.

Crime dramas :
- Bloody Monday : jdrama, cyber-attack - Adapted from the manga. I didn't watched it yet but the manga plot is really good so it should be too. The hero is a genius hacker that helps the japanese secret service.
- Ghost : kdrama, cyber-attack - About murders being solved thanks to the cyber investigation departement.
- Guilty Akuma To Keiyakushita Onna : jdrama - Maybe a bit slower than other ones but I always recommend it. It's a very interesting drama.
- H.I.T. : kdrama, also romance - HIT stands for Homicide Investigation Team, I watched it long ago but I remember it was about a serial killer. It may have grew a bit old but it was a good one.
- Pinocchio : kdrama, romance - same writer, same director, same main actor as I Hear Your Voice. It feels like another I Hear Your Voice but with different settings. This one is about journalism.
- Spotlight : kdrama - Also about journalism. Underated in my opinion.
- When It's at night : kdrama - About the Cultural Theft Departement
- Who are you (highly recommended) : kdrama, supernatural and romance - After a 6 years coma, a cop wake up being able to see ghosts.
- Nine : nine times time-travel (cf above)
- Arang and the Magistrate (cf bellow)

Supernatural dramas :
- Arang and the Magistrate (highly recommended): kdrama, historical, romance and crime - The "Magistrate" can see ghosts but don't like them. Unfortunately, Arang doesn't care about that and wants him to find out who murdered her.
- A Werewolf Boy : kmovie, romance - As the title says, about a werewolf. The rythm is slow but it's a beautiful movie.
- Gu Family Book (highly recommended) : kdrama, historical, romance and action - One day, a man living alone in a mountain discover he's half a gumiho (nine-tailed fox). He is determined to become a full human.
- Faith (cf above)
- Who are you (cf above)

First of all I reallyyyy second Faith. It's such an amazing drama <3

Here are a few more:
Supernatural:
-Orthros no Inu (j-drama): one person has a hand that kills if he touches anyone, another person can heal anyone by touching him/her.
-I Hear Your Voice (k-drama): the main character can hear other people's voices. he also seeks to help and protect a young lawyer from his father's killer (who she testified against in court and wants revenge on her once he's out of prison).
-Orange Marmalde (k-drama): basically romance story with vampires. I'm watching it right now, and it's quite confusing plot wise (it seems they split the drama in 3 different plots..?) but the concept is interesting and the characters & their interactions are nice. also, there's a plot that's in the past but I don't think it would qualify as time travel *-*
-Only You Can Hear Me (j-movie): a girl & guy communicate via telepathy.
-Moon Child (j-movie): a story about crime & vampires.
-The Master's Sun (k-drama): hilarious story of a girl who sees ghosts and a guy who enables the girl to not see ghosts when she touches him 

Time travel:
-Rooftop Prince (k-drama): (also a bit of a crime drama) a prince from joseon & his 3 friends suddenly are in the present time and they understand that they must solve the mystery behind the crown princess' death in order to go back (also features the alter egos of several characters from the past and present).
-Splah Splah Love (k-webdrama): a girl who is afraid of failing her university entrance exam suddenly travels back in time through a water puddle. It's hilarious and really worth the watch. And it's short :P

Crime:
-Hwayi: A Monster Boy (k-movie): Story of a kid that is raised by a gang of criminals who raise him into a killer. 
-Kiss Me, Kill Me (k-movie): A girl hires a professional killer to commit suicide, he refuses. Complicated love story ensues. 
-The Man From Nowhere (k-movie): A guy that was previously in the crime world but quit gets involved with it again when he has to protect his kid neighbour.
-I Hear Your Voice (see above) 
-Moon Child (see above)

Hope it helps!

PS. Oops didn't read your original posts very carefully & only checked your completed list. So there a few I listed that you know already, just ignore them :P

Kimi to Ita Mirai no Tame ni - a guy travels several times in the past, trying to correct his past mistakes and change his future
Juunen Saki mo Kimi ni Koishite - a guy travels back from the future and tries to prevent his past self from meeting his future wife
Oh My Ghost - a romance with some supernatural elements and with a tragic past incident
The Girl Who Sees Scents - the title says it all
Falling for Innocence - a guy who undergoes a heart transplant starts to act and feel like his donor
Who Are You? - it's about the relationship between a father and his daughter after he dies and enters the body of a random guy, and the following encounters between those two
Please Come Back, Mister - it's still airing, but it's really interesting and very well-done so far and it's about two men who die unexpectedly and they come back to life by posessing a female and a male
Remember – War of the Son - about a man who remembers every day in great detail
A Different Kind of Pretty Man - after a big tragic accident, a group of friends obtain some supernatural abilities and they try to discover and understand what's happening to them
Satorare - a guy whose thoughts can be heard by everyone around him
The Memorandum of Kyoko Okitegami - about a female detective who forgets everything that happened within a day when she sleeps
49 - a high school student is possed by his dead father
Yamada kun to 7 nin no Majo - it's about some highschool students who can switch bodies when they kiss
Mirai Nikki - a boy and some other several people obtain a future diary

...and I second I Hear Your Voice~ it's really good. I hope you'll like at least some of these! :)

BORDER - crime/supernatural
Keizoku 2 SPEC - crime/supernatural
Ghost - cyber crime
MOZU Season 1 - crime
Kurokouchi - crime
S Saigo no Kaikan - crime
SP - crime