The answer to this question all depends on the company you use to send and receive your e-mail. Below is a short list of different recommendations 
 
Cancel / Unsubscribe

Many e-mail services, especially online e-mail services will have an option to cancel or unsubscribe from their service. Try locating this option within the company's web page to cancel your account.
 
Don't use the e-mail account
If you do not use your e-mail for several weeks / months the e-mail account will automatically expire on almost every online e-mail service. Microsoft Hotmail, Gmail, Yahoo mail, etc. are all examples of services that will cancel your e-mail account if inactive.
 
Contact the company
If none of the above recommendations help try contacting your company directly and ask the company to cancel your account.
 
Stop paying
If you're paying for your e-mail account stop all payments to the company providing your e-mail.