"Log on" and "log in" are phrasal verbs (verbs with prepositions attached) used to denote the action of authenticating your credentials.
The general consensus of the networking community is that "log in" versus "log on" has to do with the amount of interaction you are going to have with it. "Logging in" implies little to no interaction, while "logging on" implies interaction at a near-realtime speed, usually interacting with another person who is also logged on.
Case in point: you log on to (not "onto") your computer, you log on to chatrooms; you log in to your email, you log in to a website.
In recent years, there has been more of a move to the term "sign in" which is generally thought to be more user friendly. Which coincides with the move of "register" to "sign up."
|NY Times:||log in|
digg.com: login (title, with a "Go" button)
Apple has a "login" link and a "sign in" button.
Oddly enough, LiveJournal's spellcheck doesn't recognize "logon" or "login" as words and suggests "log-on," "log on," "log-in," and "log in," respectively.
Later I will talk about the proper uses of quotation marks because I don't think I've ever used so many in a single entry.