The annoying thing about logging in is remembering both one's user name and password. With having to remember Pin numbers, phone numbers, the names of co-workers, email addresses and how much salt to add to a pan of pasta, it's a good thing we have Everything to deposit all the information we don't have brain capacity for anymore.
five year update! 5 August 2005 ...there was once other writeups here.
Most websites nowadays have the words 'log in' on it.
To 'log in' means simply to enter your name in a 'log' or diary when you enter a room, and has been adopted by computer users for when one enters a name and password to 'enter' a website.
Over at wikipedia.com, it is mentioned that 'log in' came from 'clock in', when one had a timesheet stamped when they entered their place of work, and that works as an explanation as well.
By 'logging in' to a website or a computer terminal, you are identifying yourself and giving an audit trail of your usage.