My preferences (less popular, but many cool websites are using this convention):
[Sign In] [Join]
Welcome, UserName! [Sign Out]
I wouldn't use any of the following: Log On, Logon, Log In, Log Out
Another option is (which is by the way more popular):
[Login] [Register]
Welcome, UserName! [Logout]
Google Stats (hits):
[Sign In], [Sign Out] -> 1 210 000 000 + 300 700 000 = 1 510 700 000
[Login], [Logout] -> 1 940 000 000 + 88 200 000 = 2 028 200 000
[Log In], [Log Out] -> 873 000 000 + 83 800 000 = 956 800 000
[Sign Up] for registration link is also a good option but it does't look good near [Sign In], you should use it wether with [Login] or seporatly.
[Sign In] [Join] on a page looks more user-friendly (less official) for me than [Login] [Register]