How safe are FTP servers?

FTP sends all data, including credentials over cleartext. It's a bad idea to use it. I could enumerate the reasons why here, but instead, I'll refer to you to the always enlightening http://mywiki.wooledge.org/FtpMustDie.

FTPS (FTP over SSL) is better, but if you're going to the trouble of setting that up, don't bother. Just use sftp, the server for which is already provided by your distro's ssh daemon. From the client's perspective, SFTP works in a nearly identical fashion to FTP, but it can take advantage of strong authentication (you do have password auth turned off, don't you?), as well as encryption all data including credentials.

If you're serving files to the public via HTTP (without requiring a user/pass), then running an anonymous FTP server to serve those very same files via FTP is no less safe. SFTP is preferred over FTP in cases where users need to provide login credentials.

I have password auth turned off, as well as root login, but like dcraig said I will be serving files to the public without requiring a user name/password but I was planning on doing it over https.

I've seen other sites do this and I was not required to login. If SFTP requires users to provide login credentials it sounds like my only option might be to go with FTPS.

SFTP/FTPS has nothing to do with HTTPS. They're two different things, entirely.

Why do you think you need any form of FTP?

Yeah, after thinking it over I decided that this is probably a bad idea. I don't know what I was thinking, probably that somehow FTP would be the backend and the data would be transported using http or https.