The is from the imgur FAQ:
Can I delete an image after I upload it?
Yes. At the bottom of the page, after you upload your image, you will see a section entitled "Deletion Links" that will contain everything you need to delete your image. However, be aware that this section only shows up immediately after you upload your image. This is to ensure that only you have seen them, and that only you are able to delete the image.
If you have an account, then visit this page for info on how to delete your account images.
If you have lost your deletion links, you can still have your images deleted if you file a deletion claim here: http://imgur.com/removalrequest