Yes: there is usually a "terminate mail account" link within the account administration of most email accounts. You will probably have to enter your username/password, answer your account retrieval question and enter a CAPTCHA code to finalise the process: this is required incase someone accidentally manages to access your account, or someone with malicious intent does.
What should be noted is that once you do delete an email account it cannot be reactivated; the result of the termination procedure will be permanent. However, it may be possible to register an account with the same name; therefore, old contacts may still be able to message you if you decide to change your mind.
On the whole most users do not go through the process of terminating the email account. Instead, they usually allow the account to become inactive, and after 6-12 months of inactivity, the account provider will usually wipe the account clean. However, the advantage with letting an account go inactive, is that mail providers usually do not allow the same account name to be registered. This means, that in 12-24 months time, you can usually reactivate the account name and start again.
Be sure to double check your email account is not tied to a number of other online services before deleting it - amazon, ebay etc. It could become extremely problematic if it is, and you have deleted it: you could end up in a situation where you cannot reset the password on these accounts.