Helping people with computers... one answer at a time.
Depending on the email service that you're using and how much effort you want to put into it, changing your email address can either be fairly easy or fairly hard.
How do I change my email address?
Often with free email services, people aren't happy with the email addresses that are available. After a while, they want a new email address that's "cooler" or more descriptive.
Depending on the email service that you're using and how much effort you want to put into things, changing your email address can be either easy or hard. More likely, it'll be somewhere in between.
HotMail, Yahoo, and other free services: There's really no way to change an email address. The best that you can do is create a new account with a new name, and start using it, and at the same time, simply stop using the old account with the old name. Remember, these are free and you get what you pay for.
AOL, MSN, Earthlink and other large ISPs: Because these are services that you do pay for, they often have some more flexibility. Unfortunately, it's often your email address that identifies your account with these services, so if you want a new email address, you need to create a new account. Much like the free services above, you would then start using the new account and email address and stop using the old account and email address. The good news here is that unlike the free services, most major ISPs have email forwarding services available, so that email sent to your old account can be automatically forwarded to your new one. It's also worth checking with the ISP directly - some may support a more complete solution to changing your email address - but exactly if, how, and how much will vary widely.
Small ISPs: There are thousands of small internet service providers out there who are providing connectivity to large numbers of people. The only advice that I have here is to ask them. They may be of no help at all (in which case, you'd simply create a new account with a new name and phase out your old account), or they may bend over backwards to help you make the transition transparently. There's no standard solution, so what they provide will vary greatly. Ask them.
But all of the cool names are taken!
Yes, they are.
When you go to a major ISP or free email service, thousands, perhaps millions, of people were there ahead of you. All the simple, easy to remember or "cool" names are already in use by someone else. That's why when you ask for your first name as an email name, the service may respond by recommending instead that name followed by a string of random numbers. "Leo" is probably taken, but "Leo83545" may not be. There's simply no way around this, other than perhaps trying different variations or different free services until you find something you like. Pay services are probably even less flexible and may simply assign you a name without any flexibility.
The most bullet-proof solution is to register your own domain name. If you're even a little internet-savvy, it's not difficult to do so yourself, and many ISPs will also do it for you. For an annual fee, you get your own internet domain, like example.com. Most registrars and ISPs will then provide email forwarding, so that "email@example.com" can automatically be forwarded to whatever your real email account is. Even if you change your real email from a free Hotmail account to a Yahoo account to an MSN or AOL account - changing where "firstname.lastname@example.org" goes to means your email will always reach you.
And when you have your own domain name, all email addresses on that domain are yours to do with as you wish.
Even the cool ones.
Update: - I've added a new article that explores this topic in more depth for MSN Hotmail users: How do I change my Hotmail name or address?