If you have a visible (static) internet address, then yes you can. If you don't then it isn't so easy. Contact your ISP about obtaining a static IP address if you want to host your own email (or other, such as web) server. It will cost you some extra $$ most likely.
thanks rubberman. but what I really mean is it possible to completely create an email service? I know you can register emails when you buy a domain... but can you use a static ip to host your own email accounts? I'm sorryy, this is probably a stupid question... I got kicked off of stack exchange for asking it... I would just like some information. Thanks!
For you to host your own email service, you need a few items...
1) domain name
2) DNS zone
3) static IP address
4) server running an email service application.
5) an ISP that allows you to receive/send traffic on port 25 (most do)
You start with the domain name. After you register the domain name, you need to establish the DNS zone. The easiest way is to host your DNS zone with your domain name provider. Most of them provide a self-managed DNS zone. If yours doesnt, you'll need to host your zone somewhere where you can edit the DNS records. Next, in your zone, you'll need a few important records. For email, the most important is the MX record. The MX record is used to point to your mail server. When mail systems out on the Internet receive mail that is destined for your domain, they perform a DNS lookup on your domain and search for the MX record to determine the host that they will send the mail to. This host is the one that has the public IP address assigned to it.
For most people that only get one static IP address from their ISP, this is the IP that is bound to the Internet router. On your internet router, you need to create a port forwarding rule that translates this public IP to your server's private IP address on your network on PORT 25 (SMTP).
Your server receives the traffic and since its running an email service application, does it its supposed to do.
Most importantly with email...make sure you secure your server. Do not allow an open relay. If a spammer finds your server (which they are always looking for people that setup mail servers with little expereince) and it allows for relaying mail, they will use your server and spam the world. Your ISP as well as others will be very upset and blacklist your IP. Your ISP will also most likely shut you down. In some cases, ISPs do not allow outbound 25 traffic for this reason. Many do though.
When you have the server up and running, you then create your email accounts. Since you own the domain, you create whatever accounts you want. firstname.lastname@example.org, etc...
If you like pulling your own hair, you can most definitely do it yourself!
JorgeM gave good advice, but didn't explain item #4, which is the hard part.
There are several components to full email service, and all of them need to work together to create the email experience you are accustomed to (gmail for example). Most people would be surprised at what they take for granted with email. Identify what you need from your email, then let Google lead the way. Get ready for some reading.
If its just for you and maybe 1-5 other accounts its not so bad. Default POSTFIX/Courier setup is pretty decent out of the box, and doesn't require too much configuration.
It when you want things like lots of changing users, multiple domains, virtual users, virtual domains, spam filters, anti-virus filters, or webmail interface (then you also need working HTTP server); it can get pretty crazy aligning all of the components properly.
Its really almost not worth hosting your own email server unless you are willing to buy some pre-packaged software, or unless you have really good reasons, or unless you like a challenge.
I think the answer to your underlying question is that no, you can not have an email address of <something>@<your.IP.address>. You need to have a domain name to run an email service. Plus, if I received an email with an IP address instead of a domain name, I would not touch it with my least favorite persons email program.
If you are sending email internally with in your network then the domain name does not matter, choose one like example.com which is a reserved domain and send away.
Petzold, I would love to pull my hair. Thank you very much for your information. I'm sure this will be enough to get me going. It's extremely frustrating when people tell you it's too hard to be done and not to try. Thank you for giving me the information I asked for. I appreciate it.