Almost all employers require some kind of drug test. Some will test as early as a second interview at the employer's own testing facility; others will test as part of the pre-employment physical that is required by most group insurance plans. Though such tests may make you feel a little uncomfortable, keep in mind that they are testing everyone, not just you, so don't take it as a personal insult or accusation.
Don't worry that employers may learn about prescription drugs you are taking. Testing laboratories may report only a pass or fail on tests designed to detect controlled substances. Be sure to tell the technician about any medications you are taking to assure accurate test results. Drug testing is discussed in the interviewing techniques workshop, or you can refer to the Career Services handout on Drug Screening.