Types of Free Email Service

Web-Based Email

Usually fully functional email products, including folders, address books, filters, attachments, etc
Can be accessed from any computer that has a Web browser
Great for people that do not own a computer but are able to access one, either at college, university, a library, a cyber-cafe, etc. or who have WWW access but are unable to access POP3 accounts from their computer
Require you to do all your emailing online, which may be expensive (and slow!) for some people
Tend to add a "tagline" advertisement at the end of outgoing emails
Includes such systems as Google's Gmail, Microsoft's Hotmail and Yahoo mail

Only requires a computer and modem, Internet access is not necessary
Also requires installation of free proprietary software
Displays advertising to pay for the service
Has limited features
Cheap
The most widespread system in the USA is NetZero, which offers 10 hours free every month

Your mailbox is on another computer (called a 'server'), which you can access
Usually requires email software such as Eudora and Netscape Communicator or Outlook Express
Mail is downloaded to your computer when it is retrieved
Most of your work is done offline
Most ISPs give free POP3 accounts
A good POP3 provider worth trying is FastMail.fm

Notes:

POP3 refers to incoming mail, the equivalent for outgoing mail is SMTP. Not all POP3 systems, however, allow you to send outgoing mail.
Many POP3 providers use a feature called "POP before SMTP" which requires that a person fist log in via POP before they are allowed to send through the SMTP server. This is done in order to stop Spammers from abusing their systems.

Forward incoming emails on to another email address
Useful for people who change their email address regularly
Enables you to have a constant 'virtual' address even if your 'real' address changes
The best forwarding system is probably Bigfoot

Offer email, fax and possibly voicemail, all within one "unified" mailbox
Phone-activated mailbox allowing you to hear your voicemail and sometimes even your email messages over the phone as well as over the Internet
May provide the ability to make free long-distance phone calls, with certain limitations
Although it's only free for a 30-day trial period, a very popular example of such a service is eFax