The UAE's zero tolerance policy towards drug taking and possession seems to have tightened up considerably recently. Tourists coming into and transiting through the country are under scrutiny, with new drug detection equipment in use at airports and ports of entry.
Some medicines which are available over the counter or on prescription in the home country of the tourist are on a banned or controlled list in the UAE, and travellers need to familiarise themselves with the medicines on that list. Many remedies for coughs and colds (especially anything which contains codeine), some anti-depressants, sleeping pills, painkillers and hormone replacement therapy drugs are banned in the UAE. As a visitor, you should not carry any of the banned narcotics and you should have a prescription from your doctor with you if you are bringing any of the controlled medicines into the country.
In addition, poppy seeds, betel leaves and betel nuts are also banned. The minimum sentence for any drug related crime is 4 years.
Travel agents do not always know or do not always inform potential tourists of the rules, so it is better to check with the UAE embassy in your home country before travelling. The most up-to-date list available at the moment accompanies an article on the Fair Trials website.