Based on google trends, "login" is used 9 times more than "sign in".

"log in", "log on", "logon" and "sign on" have under 1% usage.

Nevertheless, there are two countries that prefer "sign in" over "login": France and Turkey.

Although Jakob Nielsen recommended in 2002 the use of "sign in" / "sign out" over "log in" / "log out", the dialog principles of the ISO 9241-110 norm recommends that design should be in conformity with user expectations. In other words: if everyone is doing it, you should also do it.

Another important dialog principle is the error tolerance. Having "login" and "sign up" will avoid capture slips as recommended in Peter's answer

Based on google trends, "login" is used 9 times more than "sign in".

Nevertheless, there are two countries that prefer "sign in" over "login": France and Turkey.

"sign in" is used 50% more than "log in".

"log on", "logon" and "sign on" are not widely used.

Although Jakob Nielsen recommended in 2002 the use of "sign in" / "sign out" over "log in" / "log out", the dialog principles of the ISO 9241-110 norm recommends that design should be in conformity with user expectations. In other words: if everyone is doing it, you should also do it.

Another important dialog principle is the error tolerance. Having "login" and "sign up" will avoid capture slips as recommended in Peter's answer

In summary: Use "Login" for the title of your pages and links, "Log in" in the buttons to log in and "Sign up" to create a new user account.

Based on google trends, "login" is used 75% more than "sign in".

"log in", "log on", "logon" and "sign on" have under 1% usage.

Nevertheless, there are two countries that prefer "sign in" over "login": France and Turkey.

Although Jakob Nielsen recommended in 2002 the use of "sign in" / "sign out" over "log in" / "log out", the dialog principles of the ISO 9241-110 norm recommends that design should be in conformity with user expectations. In other words: if everyone is doing it, you should also do it.

Another important dialog principle is the error tolerance. Having "login" and "sign up" will avoid capture slips as recommended in Peter's answer

Based on google trends, "login" is used 9 times more than "sign in".

"log in", "log on", "logon" and "sign on" have under 1% usage.

Nevertheless, there are two countries that prefer "sign in" over "login": France and Turkey.

Although Jakob Nielsen recommended in 2002 the use of "sign in" / "sign out" over "log in" / "log out", the dialog principles of the ISO 9241-110 norm recommends that design should be in conformity with user expectations. In other words: if everyone is doing it, you should also do it.

Another important dialog principle is the error tolerance. Having "login" and "sign up" will avoid capture slips as recommended in Peter's answer