I used $_SESSION[\'name\'] to handle data from page to page. I mainly used it to keep the user logged in between pages. Within every page, i check if $_SESSION[logged_in\']
Your code is vulnerable to session fixation and session hijacking attacks. See http://phpsec.org/projects/guide/4.html for more information.
As you build bigger, more involved applications, you will also want to be careful how you handle logging the user out and handling other session-related aspects, such as privilege escalation. Handling sessions and logins safely is a tricky beast.
Implementing secure authentication is hard. Unless you are doing it as an academic exercise, i would strongly recommend using the library provided by your framework, if you are lucky enough to have a good one.
You will also want to consider things such as the following: