Not surprisingly, the app has been popular among teens and twenty-somethings who often use the service to send NSFW pictures of themselves (or others)--in other words, "sexting." People like to think that using Snapchat (instead of plain old "text & pic" messages) from their phones to send pictures of their boobs and dicks to other people is somehow safe because the picture disappears after a preset period of time. The truth is that it's not.
And, here's why (NSFW). The guy's notorious for his previous site--the textbook example of "revenge porn," being sent ostensibly with the malicious intent of hurting someone else or nuking their reputations.
This of course isn't even addressing the owners and operators of the service; what's to say that they may be keeping a copy available (even if it's ostensibly in case law enforcement or the courts issue orders for them)? Do you--or should you trust the proprietors of the service to not leak your pictures out to the masses by keeping their servers and infrastructure properly secured?
Now, I am by no means a prude. But, I work as an IT guy for a small company. Nevertheless, my firm naturally has data that is confidential and could be seriously damaging to other people if released. Yet, every person has a role in ensuring that data is secure; a leak by a single employee could literally destroy the entire firm and every ounce of goodwill that everyone associated with it has--all in a matter of days.
So too everyone has confidential data. Arguably one of these pieces of data would be images that depict someone either naked or in some private state of undress, particularly if that someone isn't actively trying to make such a depiction public. As they say, a picture is indeed worth a thousand words.
What's the moral of this little story? Be careful who you choose to be intimate with, and genuinely mutual trust is worth more than its weight in gold. And, to make a long story short: if you don't fully trust that your partner's going to keep those topless or nudie shots of you to their own self, it's best NOT to take any such pictures at all.