Not all drugs are accepted in the UAE, and some only with prescription, although some are administered in UAE hospitals.
Drugs that are banned include: codeine, amphetamines, methadone, robitussin, valium, xanax, Actifed compound linctus, tamiflu, reductil, Ritalin. This is obviously a very small list, and so it is worth checking with your local UAE Embassy. If you don’t need it, don’t bring it to the UAE, even in transit. If you have to bring it, make sure you bring a prescription and letter from your doctor. If you do get ill, you can very readily get drugs in the pharmacy.
Essentially drugs that may be over the counter in your home country could be banned in the UAE. This could include many common cold and cough remedies. Various sleeping tablets, painkillers, anti-depressants and hormone replacement therapy drugs are banned in the UAE, as well as sex stimulants such as Viagra for example. Other things that are banned include poppy seeds, which you could quite easily eat on a bread roll in another country, and qat leaf, used as a stimulant for chewing, especially in Yemen.
source: http://www.grapeshisha.com/