E-mail is not just for sending marketing messages or transactional records. It can be a good way to keep in touch with customers and build a relationship, while hearing about their experience of their brand.
One way to do so is with the e-mail survey. I recently flew JetBlue Airways, and right after my flight, the airline sent me a customer satisfaction survey. The e-mail had two links: one to the Customer Survey and another to contact Customer Commitment directly. These two simple links help customers think about their experience and connect with the brand in case there was any issue. This is a great example of CRM in e-mail.
Amazon and eBay also both use e-mail for customer relationship communications. Both send follow up e-mails to purchases to encourage customers to give their feedback. eBay asks customers to review the sellers, and Amazon asks customers to review the products. These e-mails accomplish two things: They build up the customer reviews, which adds to the shopping experience on their site, as well as building the relationship with the customers.
It is this use of e-mail that keeps the brand in front of the customer and helps build the relationship.