YES! The typical Homeowners policy and most property policies include coverage for windstorm damage to your home, other structures, and personal property subject to your deductible.
Loss settlement on a damaged roof presents some unique problems for the insurance company. Roofing materials discolor with age and have a useful life of perhaps 20 to 30 years. It may be hard to match the color of the shingles that blew off the roof. The insurance company is obligated to repair or replace the damaged roof, which ever costs less and without regard to cosmetic concerns. But, most insurance companies will strike a reasonable compromise between cost and cosmetic concerns to satisfy their customer's desires.
Generally, if the shingles can be matched the roof will simply be repaired. If the shingles can not be closely matched or the damaged area is large then the entire side of the roof will be replaced with as close to a cosmetic match as possible. However, only the damaged side of the roof is replaced, not the undamaged side. If the roof is near the end of its useful life, many home owners take this opportunity to replace the undamaged side of the roof at their own expense.
If your Homeowners policy is endorsed for Replacement Cost loss settlement (and most are), the insurance company will pay the full cost to repair or replace the damaged portion of roof without deduction for depreciation.
For answers to related questions click: Wind Damage ~ Am I Covered?