Before you delete your account, make sure you have your photos backed up. You may have photos uploaded to Instagram from a phone you no longer have, or you lost. While you can use your mobile device and/or upload your photos to your Dropbox account from a desktop, there are upload caps. Instaport.me allows you to export your file as a .zip file or to other social networks, but is currently experiencing high traffic.
Now on with deleting your Instagram account.
Some or all of the Service may be supported by advertising revenue. To help us deliver interesting paid or sponsored content or promotions, you agree that a business or other entity may pay us to display your username, likeness, photos (along with any associated metadata), and/or actions you take, in connection with paid or sponsored content or promotions, without any compensation to you. If you are under the age of eighteen (18), or under any other applicable age of majority, you represent that at least one of your parents or legal guardians has also agreed to this provision (and the use of your name, likeness, username, and/or photos (along with any associated metadata)) on your behalf.