The RTF (Rich Text Format) is a fairly old (developed in 1987) document file format. So why use it?
1. It’s universal.
RTF files can open in nearly any word processor, old or new. However, some other formats “lock you in” by having unusual file formats. Although it’s now becoming common in word processors, Microsoft Word is one example, especially when trying to load files from a newer version to an older one. Source: Personal experience.
2. They cannot harbor viruses.
Unless it’s an executable file disguised as an RTF, they cannot get viruses — there’s no macros. However, Microsoft Word files can harbor viruses. Source: click.
3. They can be opened in plain text editors.
In case of emergency — say a partially corrupted file or being stuck on a computer without an RTF editor — you can open them in plain text editors, and although there will be a few funny tags, you can recover the text. Source: Personal experience.