> but if you want to do an actual "stay logged in with no password"

Wouldn't that be a session cookie (which is a strictly necessary cookie for accessing a secure area) with no expiration?

> or just not forget the user's preferred language

Why would you store the language preference client site anyhow? Isn't a better place the user profile on the server? I use the same language for the same site no matter the device I am logged in.