The problem with "Sign In" is that it reads a lot like "Sign Up" (another common web site expression).
Consumers should be accustomed to Log In and Log Out (e.g. on Mac OS X the Apple menu says "Log Out [user name]..." and the user menu has a "Login Window" item).
Sign In. Like you, I was ambivalent. I went with Login. Surprisingly, a couple friends, who don't take a particular interest in tech stuff, mentioned to me that they'd prefer Sign In, so I switched it. I still don't think it matters much.
For what it's worth, I'm going with SIGN IN. I think that sounds more consumer-y. LOG IN sounds like a corporate intranet.
I had log in and log out but recently I switched to sign in and sign out as log in just didn't seem right for my service.
Log into a machine, Sign in to a service
I use "Sign In" To me every time I see "Log In" my mind sees Logged In
I don't show it at all. I try to streamline users into tricking them to join up.
I display all functionality out right, give them as much access as I can, and when unauthenticated users try to activate functionality they are lead to a registration page using Facebook Oauth.
When working smoothly you only need 2-3 clicks to have a users registered onto your site if they are already logged into Facebook.