Snapchat can be an addictive app. There's the fun selfie filters, the
location-aware stickers, and the peace of mind that any goofy pictures
of videos you send through the app will disappear once viewed.
With
that said, Snapchat is yet another app we have to monitor and manage on
our devices. Whether you're trying to cut back on social networks, or
you simply no longer want to use Snapchat, you can delete your account
in just a few clicks.
To delete your Snapchat account, you'll need to visit snapchat.com/a/delete_account and sign into your account.

Upon
logging in, you'll see a screen similar to the one above. Enter your
username and password one last time, then click on the yellow "Delete
Account" button.
Just as quickly as your Snaps disappear, so does
your account. It's important to remember that once you delete your
account, you cannot get it back. I was able to sign up with the same
user name after deleting my account, but my friends list and
conversation list were no longer tied to the account.
Source : Cnet.com