Here's a rundown of my Dubai shopping list, and I have to admit it's the same one I usually gave to guests who came to stay:1) Silver Bedouin jewellery, khanjars and other trinkets - most of the beautiful Bedouin jewellery you'll see in Dubai comes from the UAE and Arabian Peninsula, although some also comes from Afghanistan, Pakistan and India; ask and most retailers will be honest with you. Expect to find heavy silver bangles, anklet bracelets, engraved pendants, striking necklaces and pretty bridle head-dresses. Bedouin khanjars (daggers) make a stunning souvenir; you can also buy them framed if you live somewhere with restrictions on bringing knives into the country. Also look out for intricately engraved Koran holders and little silver kohl pots with a tiny wand attached by a fine chain.
2) Emirati handicrafts - traditionally Bedouin people, Emiratis carried little with them as they moved between desert and sea, so there isn't a huge variety of local handicrafts but you will find bright red-striped camel blankets and bags (that make wonderful cushions and ottomans), simple rustic kilims, and hand-woven palm-frond baskets and shoulder bags, and - my favorite - floor mats and cone-shaped covers used for keeping the flies off the food. They're perfect for picnics.
3) Brass and copperware - even if you're not normally a fan of either you'll love all the gorgeous stuff you can buy here, from traditional Arabian coffee pots and tea pots with tiny brass cups, to big intricately engraved trays that sit on little wooden legs, to gorgeous genie lamps...
4) Oriental perfume - whether you buy the oud (scented wood) and attars (essential oils) from a stall in the souq, sold in plain label-free bottles and containers, or you visit one of the opulent Oriental perfume shops, popular with the wealthier locals, you must buy some of the heady fragrances worn by local women. They're more spicy and pungent, and therefore hard to forget. Wear them back home and you'll definitely turn heads.
5) Frankincense - you'll see Omani frankincense sold in jute sacks in the Spice Souq (that's what those small golden rocks are). It's used by Emiratis to perfume their clothes and homes. Attend a local wedding and women will walk around the room with an incense burner so you can waft incense over yourself. You can buy the frankincense by weight, sold in brown paper bags, or in a pre-packaged kit (a better souvenir) including a small burner and coal. (Magic Coal is the best.) Ahh, I can smell it now...