You cannot visit the Arabian Peninsula without trying the fruit of the palms. Dates (of the fruit variety, not of the human variety) abound in the United Arab Emirates. They are available at sweets shops and in the supermarkets.
Dates are a popular souvenir at the airport wrapped up in fancy tins and they come in numerous variety from within the country and Saudi Arabia. They are often filled with nuts or other fruit pastes and then dipped in chocolate and covered with more nuts.
A healthy energy boost, dates are often used to break the Ramadan fast each evening. I picked up these dates at the supermarket during the month of Ramadan and found them quite delicious!