A few people lost all their emails on Gmail in 2006. https://techcrunch.com/2006/12/28/gmail-disaster-reports-of-...
There have been other Gmail outages in the past though. My two favorites are:
1. The multi-hour outage in 2009 http://www.cnn.com/2009/TECH/09/01/gmail.outage/index.html?e.... 2. And one where they had to restore data from magnetic tape backups https://gmail.googleblog.com/2011/02/gmail-back-soon-for-eve....
Of course, there are other email providers too and their own outages. But I like Gmail and that's what I follow.