I have found DXM (dextromethorphan) to be very helpful in eliminating non-productive coughs. The best I've found is the Robitussin cough gels, since those don't contain other active ingredients, because sometimes several gels are required.
If it's a productive cough, i.e. bringing up flem, I personally wouldn't take anything to stop it, since it is the body trying to get rid of the infection.
Another good option for coughs is codeine. However codeine is a narcotic and can be addictive. Cough medicines used to contain codeine regularly. But now it is usually prescription only. Although in some states/areas a pharmacist can sell cough syrups containing codeine at his or her discretion.
Licorice tea also helps some people.