There are many free or very cheap email hosting services you can use today. One of the best - and free! - email services is offered by Google.
Many people have been using Google's Gmail for a while - with addresses like <name>@gmail.com - but now Google also offers a free email service on your own domain: <anything>@<yourowndomain.org>
The reliability, spam filtering and other characteristics of this email service are probably better than the ones thrown in by your ISP or included in your current web hosting package!. Google's email can be used with any regular email software using POP3 protocol (like Microsoft Outlook) - or accessed online or on many cell phones.
This service offering is called Googe Apps 
Standard Edition and offers free mailboxes with your own domain name and other services. (As a side note, Google offers additional services for a fee - see Compare editions
Signing up for a Standard Edition takes 3 steps:
- Sign in with your Google Account.
You have to have a Google Account. If you already use Google Gmail like @gmail.com, use that one. Otherwise create a new Google account.
- Choose a domain name.
You can specify your existing domain - or register a new domain. See Getting A New Domain
Assuming that you already have your own domain:
- Sign up
- Set up - Create your first administrator account
(At this stage you are creating the first mailbox which is the administrator account for this service)
After you complete the steps above, Google Apps for your domain is activated and you will see the Dashboard page. Here are some important things you should do:
- To activate Google Apps services you must verify that you own this domain. See Verifying Domain Ownership
- Create users (mailboxes) for your domain on Google Apps
- Setup DNS so that Google Apps will start handling the email for your domain.
These steps are described here: Getting started with the control panel