Is a "Login Successful" Message Necessary?

On an informational/forum website (say, similar to a StackExchange site), is it necessary to show a "login successful" message?

Clarification: On the site in question, the users can log in by clicking a "log in" button in the header. This reveals a small panel (overlaying the existing page) where they can log in. Once logged in, the "log in" button becomes a "log out" button in the header. The user never sees a dedicated "log in" page, per-se. The images below depict the current experience, which I think is along the lines of what Adriano Repetti has described in his answer: