The Survey Email
This is a special type of email. Here you let your customers know their opinion matters. Send it and ask for their help, ask what they like or dislike about your product. But keep it short. Nobody likes long questions. As compensation for their time, you can offer a reward, e.g., a discount, a free guide, an e-book, etc.
Squarespace sets a good example. They send a survey email after somebody faces a problem with their product. They also ask to give them a hand and answer some questions to improve their service.