Sounds like you've blocked or deleted cookies, which you need for automatic log on. Check your browser's settings to ensure that it allows cookies (but not third-party cookies). Having done that, go to the log-in page for the site you wish to visit and look for a tick box that says something like "Remember me on this computer". Check the box and then log in. You should be logged in automatically the next time you visit the site.
Enable cookies in Firefox by clicking Tools, then Options, and then the Privacy tab. Check the box marked "Accept cookies from sites" and click OK.
To enable cookies in IE, click Tools, then Internet Options, and then the Privacy tab. Click the Advanced button. You have the option of allowing automatic cookie handling or overriding it. To override it, check the Override... box. Under First-party cookies select Accept and under Third -party cookies select Block. (Tracking cookies are third-party cookies.) Finally click OK.
Note that you can limit cookies to those from specific trusted sites, but the method for doing that should become clear if you follow the above steps.
Hope this helps.