Is there a Linux file manager with a proper drop-down tree view? (like finder in OS X)

Nautilus does this.

Ubuntu up to version 12.10

• Just switch to View > List.

Ubuntu 13.04

Feature is missing in this release

Ubuntu 13.10 and newer

• activate Preferences > Display > Navigate folders in a tree
• switch to List View

Dolphin appears to have this capability.

You could use Marlin as well https://launchpad.net/marlin

Install with

sudo add-apt-repository ppa:marlin-devs/marlin-daily
sudo apt-get update && sudo apt-get install marlin marlin-plugin-*

UPDATE : haven't tested this, but it should work to set Marlin as the default file manager.

xdg-mime default Marlin.desktop inode/directory