Yes. You can see the browsing history from the History menu item on the Menu bar at the top of the browser window. Use Tools > Downloads to see the Downloads history.

THATS NOT WHAT I MEAN, DOES FIREFOX KEEP A HISTORY, EVEN AFTER YOU CLEAR YOURS ?

Firefox does not keep a history after you clear yours. I understand what you mean. Firefox does not send your browsing history to Mozilla. However Firefox has components from Google, like Anti-phishing. Due to these Google components, Google Privacy Policy must be followed. Read Google Privacy Policy-

1. Google Safe Browsing Policy - http://www.google.com/intl/en_us/privacy/browsing.html