There is no limit from a database perspective.
Note that a component does not really belong to a Project Area ... it just has an owner field (which determines read-access to that component) which can be set to a Project Area.  
The practical limits are usability limits in the UI.   In particular, if you have hundreds of components in a project area, stream, or workspace, scrolling through the GUI lists of components to find the one you want will be clumsy.
So ideally, 50 or fewer components in a given stream/workspace that is frequently accessed is ideal.
A few hundred in a stream/workspace that isn't accessed that frequently (in the GUI) is ok.
I personally would never put more than a few hundred in a stream/workspace.
Note that there is a high priority plan item for the SCM team to allow the definition of "hierarchical components", which should remove this constraint on the number of workspaces in a given stream/workspace.