It bothers me when sites provide links to “sign up” and “login”. The former is a verb phrase, but the latter is a noun; it should be “log in” to mirror the form. An argument can be made for linking to “login” the noun, as in the “login [page]” but then you would also link to the “signup [page]“.
The same logic applies to “logout” — don’t use it unless you’re using “login” and “signup”. Consistency is a large part of quality, so mind your verbs and nouns to ensure that all is right with the symmetry of your header copy.
I should probably consult with my friendly neighborhood linguist about what has been sufficiently bastardized evolved into accepted meaning, but for now I’ll rely on cold, heartless logic.
This is simply an issue of consistency–which is to say, good editing–and not one of logic/language change/whatever. A login is a login and you log in from the login page. That’s the only way these things work. (I.e. are “accepted meanings.”) The problem is not that people are being illogical–it’s that they don’t know there are two forms depending on whether you’re nouning or verbing. A good way to illustrate why “log in” is the verb form is that you can talk about how someone has “logged in” or will be “logging in” and not “loggedin” or “loggingin”. Making “login” the noun is meant to disambiguate it from “log in”, and make it consistent with other nouns made from phrasal verbs (e.g. the “lockup” is where they lock you up, and “backups” are what are generated when you back your data up).