It is absolutely necessary to have motor insurance in the UAE. With more than 200 nationalities driving in Dubai, quality of driving is variable and accidents do occur. In case you have caused an accident resulting in a fatality, you will be liable to pay diya (blood money) to the family of the deceased. Diya sums can range from AED 200,000 to AED 500,000 in addition to fines for damage to public property. If you are unable to pay, you may face a long prison term.
With proper motor insurance in place, you can protect yourself from such eventualities, assuming also that you are driving with a valid UAE driving license, have not consumed alcohol or drugs and your car is legally registered. There are also rare instances of injuring/killing a camel/goat etc for which diya will need to be paid to the owner.