MySQL problem (Access denied?!)

Hi! I've got MySQL runing and everything works fine when I use the client(?) as root. But if I start the client with mysql -u root -p then I get the following error (smt like): ERROR: Access denied for user 'root@localhost' (Using password: YES) Cause of this loging in as root is the only way for me to use mysql. I need to get the username+password log-in to work so that I can access my database through PHP and as another user! Should I do something with mysqladmin to get this to work? Cheers! - tk