It depends on the system. NEC-related I usually only collect PCE Engine. In that case I only want the case, the game, and the manual. The reply card and obi can suck it. I do have a few US games. In those cases I don't give two shits about the redundant pointless outer box, but I need the case.
Same goes for Saturn. With Genesis and NGP I don't do loose unless I absolutely have to (ie: Last Blade US only exists as a loose cart). With SNES its complicated. With Japanese carts I only buy games with boxes and manuals, but with US games the boxes are so much shittier by design (ie: thin cardboard, sucky art, and a box that is %40 covered in logos) that I don't have any of those. Ostensibly I collect FC boxes, but they are pretty hard to find. All my NES carts are loose.
Of course all this OCD-ness really gets frustrating when the companies themselves make proper collecting impossible. For example, pack in games that lack a case (ie: Mario Kart DS that was bundled with my DS), and later TG-16 and Genesis games where they switched to a f*cking cheap-ass cardboard box after years of selling us real cases.
I don't collect homebrew boxes, ie: sparky's lables, MVS shock boxes, etc. If it isn't official its highly unlikely I'll be interested.