Due to wide range of temperature and climatic conditions, it is advisable to bring appropriate clothing. From May to September normal traveling cloths plus a light woolen sweater or a light jacket and a light walking boots are sufficient. From November to end of April on the other hand, you will need very warm cloths including underwear or woolen tights to wear under trousers, thick socks, strong boots and down jacket.
You will be offending people if you walk around in skimpy or tight fitting clothes. Although there are normally opportunities to wear skirts or loose trousers, men should not wear singlets. During visit of monasteries, Dzongs and other religious sites, you should not wear shorts and hats.
The following is a fairly exhaustive list of what you should pack for the trip:
Clothes as per season, sunglasses/spare glasses or contact lenses, pair of casual shoes, washing kit, shaving kit, towel, hat umbrella, camera, film and accessories, maps, insect repellent, hand cream, small sewing kit & safety pins, torch or flash light with spare batteries, mirror, sun screen cream, lip salve or soluble aspirin, antiseptic cream, preparation for the relief of sunburn. You may not be tuned to the Asian drugs so it is always better to bring own brand.