I ran my own email server about 10-ish years ago for a while on a Linode using Postfix and Dovecot similar to what others have mentioned. Took some effort to prevent GMail from just flagging everything I sent as spam, but I was eventually able to do it. I remember having to configure something particular with DNS records. (An SPF TXT record, probably?)
I didn't end up using it very much and shut it down after a couple years, but it was a good exercise and I learned a lot from doing it.