I"m on windows7 and the few times that I'm forced to use IE (internet explorer) I haven't had any issue with it storing login info. I get the standard do you want us to remember it for you. However most of the time I use Firefox or I'll use chrome. You might want to check out one of those browsers, both are free and you might find you like them better (most do).

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Do you mean the Windows login screen when you're booting the computer?

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Password to login to Windows 7? It won't store it for you and neither does XP. But you can disable the thing from asking. For Windows 7, hit your Start button (bottom left). In the Run dialog box, type "control userpasswords2" (w/o quotes). Uncheck the option to require a password.