On the tab Recent Files tab in the Database Manager, you can see all files you have last accessed. This concerns both local files as well as files that were opened on e.g. an Internet Server or via Enterprise Server.
Simply select the desired file and click on OK in order to get to the window for entering the file's master password and/or key file.
NOTE: The tab Last Used is only available if the program keeps a list of the last-used files. You can (un-)check this via Options > General > Store list of last used files.