In the interest of disproving any falsehoods regarding his relationships, I have the full list here of all significant partners he has had.
You can Google for yourself his full history, if you like, but I found that unnecessary.
Take note that none of these women have ever accused him of abuse besides Heard, and besides her, they all defended him.
Lori Allison (1983-1985): Married.
Sherilyn Fenn (1985-1988): Engaged.
Jennifer Grey (1989): Dated.
Winona Ryder (1989-1993): Engaged.
Juliette Lewis (1993): Rumored to have dated.
Ellen Barkin (1994): Dated.
Kate Moss (1994-1998): Dated.
Vanessa Paradis (1998-2012): Dated and had two children, Lily-Rose and Jack.