2 things you have to follow.
Always use firefox if you are using the home computer.
Why because firefox store the username,password information inside it and whenever you wish to login anywhere, Its shows the username and password of this site. So by selecting the ids. You just signin on that page.

Other thing is about to care running applications in background. If you think that your PC in infected with any trojan or something . Boot your system in safe mode by pressing F5 and after login in Windows Go to run and type msconfig . A dialoge appears. Go to startup programs and check there what files are running with startup.
Because on safe mode its not possible for trojan,virus to make hide itselfs.
Catch and clean it. If you don't understand and want to know more about it please ask .

Good tip. But I have a question about other browsers like safari,opera . Are they are not secure like firefox ? Because inside safari,opera and new IE 7-8. They add the same feature like firefox to remember the username and password.

Yes Nic I know. But I told you for firefox because of addons. In firefox You find a addon name "Keyboard Encrypt" With this you can protect easily your keyboard strokes for leaking your username and password information on internet.But its not mean that you can use only firefox. Use others if you like.