And now it's happening with advertisement too. Tell your friend you just took a pregnancy test via FB messenger and now every advertiser on the internet knows just what to sell you. Most people don't really care about this yet, but most people don't realize that this kind of thing could be used in the future for all sorts of dystopian shit. All this data is being stored. I think Google is treating my data pretty responsibly at the moment, but I could see it being used for anything from background checks (e.g. checking search history or message logs for indicators of illegal activity) to blackmail.
On a tangential sidenote, I read an article about Snap recently about how they're trying to position themselves as a different kind of social media company. They don't (yet) perform highly sophisticated targeted advertising and don't save a lot of actual content data. You typically are only connected to your actual friends, not some random guy from your high school class, your aunt, your ex-girlfriend, and your coworker. There's also no public profile for employers to search for and snoop around. Of course these are typically the case for any tool focused on direct messaging but I hope as Snap expands they can be both successful and keep these fantastic qualities.