Question: After update, old Eclipse plugins remain in "plugins" folder (there are also leftovers in "features" folder).

Is there a way to remove those automatically?

Answer: 
To get rid of the old plugins you have to clear the Installation History. Go to Help | About Eclipse | Installation Details | Installation History and select all the old stuff. Then click delete and restart. Voila. This works with Eclipse Helios (3.6)
Eclipse allows you to revert back to any previous configuration (go to the Help menu, then "Software Updates"). My guess is that Eclipse won't remove these old versions, or this functionality would no longer work.

If when you restart Eclipse you provide the "-clean" argument, it performs various cleanup operations, but for reasons stated above I don't think it will remove old plugins/features.