After the recent news that Snapchat was hacked and users' phone numbers were stolen, you may want to cancel your Snapchat account. Snapchat doesn't want that, so they haven't made it easy for you to find the page where you can do that. Read this article to help you delete your Snapchat account.
Steps

Step #1. Open Snapchat homepage
Open a browser of your choice and then open the Snapchat homepage. The page where you can delete your account is well hidden in the 'Support' section. You cannot delete an account from the app.

Step 2. Click on 'Support'
This link can be found on the homepage, at the bottom, in the middle. Now you come to the main menu of the 'Support' section.

Step 3. Go to the page where you can delete your account
Click on the following links in succession: "Learning the Basics" → "Account Settings" → "Delete an account". Now you will be asked to login to your Snapchat account.

Step 4. Enter your password again
To permanently delete your account, you must enter your password again. Once you've done that, click on the 'Delete My Account' button. Your account has now been permanently deleted and cannot be recovered.