http://drive.google.com/uc?export=view&id=0B-XjzPgAIEuYTG9Cb3hSWHJab0k
Assuming you keep your Gmail or Dropbox forever, sure. And never move the contents inside of it, or change the share permissions. The nice thing about sites like Imgur & co is that they are permanent & historical, so they're (hopefully) going to be around forever.
http://tinypic.com/faq.phpQ: How long are images kept?
A: The images are kept until they have not been viewed for 90 days. After 90 days have elapsed, your image may be removed.
forever is a tricky word
tinypic isn't forever
http://tinypic.com/faq.php
imgur says forever*
*until death of service or takeover by another company perhaps