Email is cloud-based right from the start. For the corporate they maintain their own email systems like IBM Lotus notes and Microsoft Outlook. The pioneers in email are Yahoo and AOL. Google introduced Gmail as well as the cloud-based file system like Google Docs and Drive. I started to use Google Docs in 2008. My first email is Yahoo and that was in 2005. 

Currently, corporates are migrating to Office 365 while others use Gmail.