Being able to add fields to Media like "Copyright" or "Credits" would be great. Also the option to rename the file on the server. The ability to categorize and tag any media would be cool as well. I would like to be able to drag media to a category or at bulk edit them. Maybe only partially related: I would like to define different formats, for ex. square, proportional so I can use them accordingly.

I am not sure whether all of this should be part of core or in a separate modules. What I wouldn't like is a bloated and slow system.