All western clothing is accepted such as t-shirts, jeans, baseball caps, dress suits, shirts and pants.
Offensive, indecent and revealing clothing is not tolerated and considered disrespectful to the locals so try not to wear any very short shorts, miniskirts, revealing tops or spaghetti straps.
Traditional Arabic dress is welcome and encouraged and can often bring about a new found respect and generous hospitality, if seen being worn by western cultures or people not traditional from the Arabic culture. For women the traditional dress is called an albaya and for men it is called the kondola.
Do not wear anything that you don't want being scrutinized for. It is wise to wear long skirts and covered shoulders as this is considered respectful and often invites more generosity and hospitality from the locals.
Try wearing cotton in the summer months due to the hot and humid climate. Shorts are accepted as well so long as they are not too short this will save you from being harassed for your clothing. Natural fibres like cotton and linen work well.
Since Dubai is almost always hot, try to wear loose fitting clothing that is not tight or revealing and not only will you be respecting the culture and religion but you will also feel the heat a lot less than if you were to wear tight clothing.