Romance with Criminal

I'm looking for a drama where the main female or male lead falls in love with a criminal or criminal like character. It doesn't always have to be a female falling for the male criminal character as long as one of them in the relationship is considered to be one

Some exceptions include the main male/female lead not actually being a criminal but coming from a family of them, or them being misunderstand and treated as a criminal

Some of the ones I have watched includes:

Guilty Akuma to Keiyakushita Onna

Innocent Man

Cruel City

Healer

IRIS / IRIS 2

Maou

Ouroboros

Shark

Two Weeks

Love Around

The Masked Lover

As I have said it doesn't have to be exact, as long as it has the same or similar element it will be fine.

Korea:
East of Eden --- He works w/ mobsters and her father is his boss
Tree of Heaven --- He becomes a gangster
Haeundae Lovers ---  She's the daughter of a mob-boss
Padam Padam --- He's an ex-convict
Piano --- He's a gangster
Robber --- He's a con-man
Tazza --- He's involved w/  gangsters as a professional card player
City Hunter --- similar to Healer 
Prosecutor Princess  --- The criminal  is related to one of them.
When a Man's in Love --- He's a gangster going straight ... annoying female so it makes the plot frustrating

Japan:
Cheap Love -- He's a thug 
Gokusen --- She's the daughter of the mob-boss
Soredemo, Ikite Yuku --- Her brother is a killer, his sister is the victim.
Byakuyako --- One or both are criminals 

China: 
Too Late to Say I Love You --- He's a warlord anti-hero (not criminal) ...
Cruel Romance --- He's a gangster  .... weak characters .... I found it disappointing
Lady & Liar ---  He's a gangster .... weak writing.... I found it disappointing

Thailand:
Cheewit Puer Kah Huajai Puer Tur  --- He's a hired assassin, hit-man ... her father is the villain, a criminal ... Not much interior conflict  or character insight ... but romance works.... Feel is more that of young first-love than conflicting feelings of dealing w/ a criminal. 

Movies:
Daisy --- He's a hired hit-man.
Late Autumn ---  She's a prisoner on leave, he's a con-man ... perfect match.
Love (aka Sarang) --- He's a mobster
Love Me Not --- He's a con-man ... movie version of K-drama That Winter the Wind Blows .... I like movie better.
Oasis ---  He's a sociopath .... touching love-story
Kiss Me, Kill Me --- He's a hitman she hires to kill her ... it's a comedy
Pained --- He's a thug for hire 
White Night --- One of them is the criminal (movie version of J-dorama Byakuyako)

EDIT: +1 Ugly Alert .... +1 Family's Honor .... +1 The Princess' Man (who's the criminal, him or her father?) ...

Most of mine are listed above, but I'll add one I watched today and a current drama:

• Catch Me (movie)
• Suspicious Partner  (current airing drama)

• I will double underline that Secret is amazing, although heavy.  Ji Sung rocks it.  
• Innocent Man is amazing and not what you'd expect from Song Joong Ki.

Not sure if all of these fits the bill, especially the "criminal" part, but at least one of the leads is treated badly due to misconceptions about them:

Athena: Goddess of War – The female lead works for the antagonist, it's a spin-off from IRIS and has better production value than IRIS, although not necessarily a better story
Suspicious Partner – She's mistaken as a criminal, still on-air
The Bridal Mask – He's a Korean who works for the Japanese during the Japanese rule and Korean people treat him as a criminal
Defendant – He's accused for killing his own family, I'm on episode 3 and it's superb so far
The Guardians – Still on-air, the main female lead actually commits a crime early in the drama and after that she's on a run but still a heroine

Beautiful Mind – Like Panda said, he's not trusted because he's a doctor with a mental illness
Good Doctor – This feels like it wouldn't fit your description at all, but in the same way as Beautiful Mind, he's a doctor but he suffers from autistic savant disorder and people don't trust him
Romantic Doctor, Teacher Kim – The least "treated badly" of all these but Teacher Kim is still involved in being mistaken as a doctor who killed his patient in the past

+1 Gokusen
+1 City Hunter
although they're both quite far from being treated as "criminals" (although they both commit some kind of crimes), these two are on my all-time favorite list!