If you are using Netscape, go to Edit, Preferences then Mail and Groups, then Mail Servers. Click on Edit on the right to edit the properties of your mail account. Below the server names, check the box that says Remember Mail Password.
If you are using Outlook, go to Tools, Accounts, Mail highlight the account you want to save the password for and click Properties. Go to Servers, and put your password in the option for password there, and select Remember Password.