The harm effect on other people from ones drug use are normally associated with the drug user having to find the money to purchase illegal drugs, if the addict could just go to the local chemist and pick up what he needs then he would not be harming anyone but himself and even that is debatable .
The drugs would be more affordable and easy to get in any pharmacy, less people would resort to theft and borrowing from gangsters to fuel their addiction. They'd be getting pure product instead of some unknown and sometimes deadly chemicals. Gangsters would lose their main income and governments would get more money from taxes.
Apart from this, it has been proven that legalization and regulation lowers the level of drug addiction. For example, in Portugal, the number of drug users declined after the government legalized all sort of drugs in 2001.