I recently logged in on StackOverflow and then visited a stackexchange site where I also have an account. I used Google Chrome.
I did not receive a "Welcome back, user, you have been logged in" message. However, on a different computer, I got this message with any browser if there are no cookies.
The message seems to indicate that the site logs me in automatically. It remains unclear why this does not always happen. Can the missing message/login have to do something with different hardware or software configurations?