The best way to answer this question is to put yourself in the shoes of your customer. Why would you give your email address to someone that provides a service to you? Ultimately it depends on what it is you’ll get in return and how much trust you have in the person you’re giving it to to treat your email with the respect that you deserve.
You know your business better than anyone. Think about ways that you can deliver an improved experience to your customer that they might only be able to get via email or an Internet-based experience with you. For example, the airlines offer the option for an electronic ticket to be delivered via email so you no longer have to worry about forgetting or losing a paper ticket. A hotel may send an electronic confirmation that your reservation has been canceled, eliminating any chance of confusion.
We have seen examples where our customers have effectively obtained email addresses offering a monthly or quarterly newsletter, delivered electronically using Listen360, that includes coupons or incentives only available to those customers receiving it by email. Other examples include offering an email confirmation of an appointment, providing a warranty and follow-up program, electronic copies of invoices/receipts, etc. Again, think about your business and (if you were a customer) what additional value could be delivered using email.
You may also want to review "Gathering customer email addresses" for practical tools designed to help you acquire customer email addresses.