When you change the status of an Opportunity, Case, Sales Lead etc. the state change is not currently automatically recorded.  However, there is a workaround that can be implemented as part of your Company's Standard Operating Procedures (see below).  We also have this requirement logged on our Ideas Forum, which drives our Roadmap - the order in which we develop new features.

Please take a moment to add your vote and comments to the idea on our Ideas Forum - Record State and Status Changes & Approvals.

Here's a suggested workaround:

Whenever your staff/team change the status of an opportunity it's good practice to add a Note or Activity with a relevant description.  For example: Add a comment when moving the Opportunity from Status New to Underway - "Underway: Made initial call to prospect".  Then, when the deal is won and you're moving the "Deal Won!!: Prospect wishes to proceed an place order".

This information will be easily accessible on the Summary tab of the Opportunity.

Alternatively you could add custom fields to record the date that your opportunity moved from stage to stage.  This might not look very elegant on the record but would enable you to report on when the status changed.