Easy connectable/click system between enclosures
3 Formats come to mind:

1 - Pogos and magnets


(Image is from http://www.foxlink.com/)

When you mentioned "click" the magnet action came to mind. This is the least exerted force one, and also easiest to unplug. Not very dense, a bit expensive.

Some examples of products which use this are LitteBits and the old Macbook charger. 

2 - Board to board / Mezzanine connectors

This is probably the highest density option, missing the "click" action. Potentially the stiffest connection.



(Image is from http://www.hirose.com/)

3 - Edge connectors

I bet you remember these? They are cheap on the PCB side (and I personally have found to be expensive on the connector side unless you use PCI-express). Also missing the "click" factor.


(Image from Wiki Commons)

Other alternatives

Or just use pin headers protruding from the enclosure. I've also done a short-term project with springs and magnets in cheap a pogo-ish way - very cheap and has the "click" action.

Also, as in the MacBook charger, if you get at least N*2-1 connections, you can make the connector orientation indifferent. (As in, instead of VCC, GND, TX, you do VCC, GND, TX, GND, VCC, so you can flip it.)