You are correct that cookies do hold your username & password, but you do not have to keep the cookies. If you delete all your cookies, the next time you go to log in to say PCA you will have to re-type your username.
Deleting cookies will not stop you from accessing any Internet sites.
It is safe to delete all cookies and Temp Internet files. If you are on dial-up then it is a good policy to delete these as it will help with the speed of your connection.