Bulk install WordPress plugins, with Multi Plugin Installer
Multi Plugin Installer is a WordPress plugin that lets you install multiple plugins at once.
Unfortunately it won’t create a list of your currently installed plugins, but you can use BackWPup to create and backup such a list. Then in Multi Plugin Installer paste the names of your plugins in the text box and press the “install” button to have them all installed from the official WordPress pages one by one automatically.
Multi Plugin Installer can also install multiple plugins you may have on your PC. It can export a settings file and import it on another WordPress installation.
Although unable to save a list of your currently installed plugins, it can backup them entirely to help you install them on another WordPress installation.