Change mysql password interactively
From the mysqladmin documentation:


  In MySQL 5.6, the new password can be omitted following the password
  command. In this case, mysqladmin prompts for the password value,
  which enables you to avoid specifying the password on the command
  line. Omitting the password value should be done only if password is the final 
  command on the mysqladmin command line. Otherwise, the next argument
  is taken as the password.


In earlier versions you can't do this as those will complain for 'Too few arguments to change password' (thanks Kaarel for reporting this).  In theory you can issue a command like 

mysqladmin -u kaarel password newpass


and then it does not appear in the database logs - but may still be stored elsewhere, like .bash_history.