This question can be answered in several different ways depending if the focus is on illicit drugs (heroin, cocaine), medicinal drugs (warfarin, insulin), or over-the-counter drugs (aspirin, decongestants). The difference is in the purpose of record-taking and its effect on the taker; for the purposes of this question, the focus will be on drug interaction. For example, aspirin is a common OTC pain reliever, but should not be taken by people on prescription blood thinners (warfarin) because it acts to boost the thinning beyond proper measurements. This can cause hemophilia, or the inability to clot.
The most important reason for drug records is the ability of the medical provider to judge health and drug interactions. Records of drugs taken in the past and being currently taken allow doctors to know what changes the body has undergone in the past; some narcotics raise a patient's tolerance to anesthetics, making surgery and pain management difficult. Another good effect of record-keeping is the ability for doctors and law-enforcement to quickly and accurately see what drugs have been used and when; this gives a pattern of behavior for treatment and/or legal counsel. Food allergies or food interactions with drugs can also cause problems, and so records show food/drug interactions and safety. Another reason is for statistics nationwide; by knowing the prevalence and locality of drug habits, law enforcement can more easily track and eliminate illegal drug suppliers.
If you mean drugs as in jotting down all the medications you have taken then it is really important that you jot it down you frequently take other medications as well. It enables a doctor to assess the patients prognosis correctly and whether the extra medication is effecting you taking other medications.