The fastest way is to set up "Vacation responder" in Settings is such a way that it looks like the account doesn't exist anymore. Otherwise, just send your request to Gmail team.

1) go to your Google web home page
2) click on the My Account link at the upper right
3) at the bottom of My Account click on help which takes you to the My Accounts help page
4) under the Managing Your Gooogle Account heading find Deleting and click there
5) the page that pops up presents you with the option of deleting your Google account entirely or only gmail

Here is a link from google's help page.
http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=61177

Next time just click the service's help section.  Any online email (gmail, yahoo, hotmail, etc) can be closed.

...but guess what?  You may have deleted all those emails, "cleaned up" a record, so you think.

Most likely your emails are all still sitting in storage in a massive tape archive for many years to come.  A subpoena can force Google to retrieve those if need be.