to the best of my knowledge, mail servers require a domainname in their configuration. If you don't have your own, what will you set it to? Also, how will people reply to the email?
By the way, registering a domainname and setting up dynamic dns is easy and cheap. You register a domain name for around $8/year. also, most dynamic dns services have a 1 time setup fee; usually $20-$40. So, you could have a domain for say, 5 years, and it will cost you a total of $60 at the most.