Depends on whether you're a collector or just an enthusiast.
Some folks don't even need the disks/cartridges...just an SD or Compact Flash filled with as many titles as they can download is good enough. As long as they're accessible they don't care what physical software they have.
Others place a high value on having sealed boxes with all the goodies safe and sound inside, never to be seen by human eyes again.
Me, I slice the shrink wrap immediately (shrink wrap damages more frail boxes with time - it's called 'shrink' wrap for a reason), and remove the contents. I figure all cartridges should be plugged in and played at least once - even if I have a digital copy as my primary use version. I also like to display my collection.
The carts I then put in an audio-cassette bookcase (found a six-shelf unit from Sauder* that fits EXACTLY 35 carts per shelf like it was made for them). The boxes are displayed in bookcases and wall shelves. Except for TI-branded boxes which are generic and not worth displaying - I really don't even care if I get a box when buying TI released carts (except for the binder-enclosed ones).
The manuals and instruction cards are kept in sealed zip-lock bags (bought 1000 6x9 bags in bulk for next to nothing). Most TI manuals are exactly the right size to then be placed in mens' shoeboxes (kinda like a mini version of a comic book store bin).
So it all depends on how you view your collection.
One thing is certain...paper products NEED to be sealed or they dry out, yellow and eventually fall apart. My mother left me hundreds of 1940's Hit Parader magazines (music fan mags with lyrics of popular songs) but she just kept them stored in boxes. I opened one of those boxes a few months ago, and it was sad how badly these 70-80 year old magazines had disintegrated. They are literally worthless now (pages fall apart in my hands as I flip through), but could have been saved easily by sealing them before boxing them (never assume mother knows best).
So if you DO keep manuals, zip-lock (or similar air tight storage) is a must. They might look just a bit yellow after 35 years, but what about in another 35???
*(Sauder is kinda like Ikea except all products are made in North America)