In many cases, "go to Web site X" is more accurate than "log on to Web site X." If you're entering a username and a password, fine. But beyond that, there's just no "logging in" going on.
And then we have the question of using one word or two.
"Login," "logon," "logout," and "logoff" function as adjectives:
This is our logout page.
Update your login information.
"Log in," "log on," "log out," and "log off" function as verbs ("verb phrases" if you want to get technical):
Log in here.
You should log off before you leave work.
You also want the two-word forms for verbals (a verbal is a noun or an adjective that was derived from a verb):
Logging in is easy. (Here, "logging in" is a noun. It's the thing that is [verb] easy [adjective].)