If a company provides a product or service free gratis, is the cost or value of that product or service deductible?

Assuming this donation is being made to a 501(c)(3) organization: If the product is something you make in the course of your business, so that you are essentially donating something from inventory, then you may deduct the lesser of its market value or your cost of manufacture. As for donating services - only the out-of-pocket expenses you incur that are necessary to provide the service are deductible (such as mileage, cost of supplies, wages paid to employees, etc.).