Is there any online source that displays the change in world crime rates since the Middle Ages? I am also looking for attempted crime, not "successful" crime, since the rate of successful murders may be confused by the improvement of medical sciences over the years.
Here is a figure of homicide rates from Stephen Pinker's Better Angels of our Nature:
I wouldn't worry about medical science interfering with these trends much, as doctors were as likely to hurt patients as help them until the 19th century.
Really high quality crime stats only started to be collected in the 19th century, so Pinker's measures here are about as good as we can do AFAIK.