As you may already know from Hotmail sign in, whenever you login to your email account, you have the option of making Windows Live automatically remember your user name (the Windows Live ID, or email address), and password, so that you don't have to enter them manually each time you want to check your emails. The Hotmail automatic login option is very convenient, but has some security drawbacks to consider, especially when checking email messages from a shared or public computer - this tutorial helps you decide when you should automatically sign in to your Hotmail account, and when you should avoid this feature.
When you are logged out of your Hotmail account, or accessing it for the first time on a computer, you will see the sign in pictured below when you type "www.hotmail.com" or "www.live.com" in your web browser's address bar; and this is also the case, of course, if you sign in to Windows Live Hotmail without making it remember your user name (Windows Live ID, or email address), and/or password.
If you are checking your emails from your own computer, or a computer accessed only by people you trust, you can safely make Hotmail remember your credentials: the "least safe" option is to remember both your email address and password - this means that whenever someone types the address of the Hotmail or Windows Live homepage in that browser, they will automatically login to Hotmail! The safer of these two alternatives is to only check the "Remember me" checkbox, and leave the "Remember my password" unchecked: that way, when the sign in form loads, it will have your email address pre-filled, but you will still have to manually type in your account password.
Again, this question boils down to how much your trust people who have access to your computer, and can login to your user profile (under your own user name, if they know the password or if Windows / Mac OS X is set not to ask for a password to login).
But, as a general rule, you should always avoid using the remember me / remember my password options for Hotmail on a computer that isn't yours; and you should never enable that option when you are checking your Windows Live Hotmail account from a public computer (for example at school, on a shared computer at work, at the library, and other unfamiliar locations).
So, while the Hotmail automatic login option is a very convenient solution when your computer itself is protected, you should avoid at all cost having Hotmail automatically sign in on any other computer, and any circumstance where you would not leave your wallet unattended on the table (a good rule of thumb!)
Sign-in Tip: most modern web browsers for Windows 7 / Vista / XP, Mac OS X, or Linux (Ubuntu, SUSE or other distribution), include a form manager functionality that lets you remember your user names and passwords for sign in forms: the same safety tips apply in that case. And, if you login to Hotmail from a computer other than yours, always confirm that you are completely signed out of your account before leaving!