As a rule of thumb (especially for women) chest, shoulders, and knees should be covered when not at beach resorts, so it's a good idea to pack tops with sleeves, long dresses and skirts and loose-fitting trousers. Men can opt for lightweight trousers and short-sleeved shirts.
Should I carry my passport with me in Egypt?
In Egypt, carry your passport with you: you'll need it to register at hotels, change money at banks, and possibly to show at police checkpoints. If travelling for any length of time, it may be worth registering with your embassy in Cairo, which will help speed things up if you lose your passport.