Most owners keep something in the garage for the exhaust and never look at it again until a joint is apart and a gasket has torn. The question worth asking is not what might be useful but what will certainly be destroyed the moment it is disturbed. That is a much shorter list, and it is the only list worth storing.
A spare earns its place when the original part cannot survive removal, when it is specific to one joint, and when not having it stops the car. Anything that can be bought locally on a weekday morning does not need to live in a box for years.
Crush gaskets, the soft metal or composite rings that sit between flanges, are shaped once by clamping force. When the joint is opened, the ring has already taken a set and its sealing surface is no longer flat. Reusing it is not a gamble on quality but on whether the crush pattern lines up again, and it rarely does.
Those are the gaskets to keep: the ones matched to a flange you own, in the material the joint was built for. A stack of random rings from previous jobs is worse than none, because the wrong one will be fitted at the wrong moment.
A clamp that has been tightened and released keeps a memory of the shape it held. Band clamps stretch, worm-drive clamps bite a track into themselves, and V-band clamps lose the even contact that makes them work. Small amounts of this are recoverable, and the second and third reuse of the same clamp is where leaks begin.
Keep new clamps of the sizes your joints actually use, in the type each joint needs. A clamp that has already been on and off a joint more than a few times belongs in the scrap rather than in the spares box, because it will be the one you reach for in a hurry.
Rubber and composite parts age on the shelf as surely as they do on the car. They harden, they take a set from being stored bent, and they absorb whatever is in the air around them. Sealing them in a bag away from sunlight and ozone does more for their life than any label.
Metal parts are the opposite. A clamp or a steel gasket will sit for a long time if it stays dry, and it will rust in a damp drawer. Coated parts should not be stored where the coating can be scratched off against other hardware.
The most common failure with spares is a part that is nearly right. A ring that almost matches the flange bore, or a clamp that almost matches the outside diameter, will be forced into service and will leak. The spare has to be identified with the joint it belongs to, not by size alone.
Label the bag with the joint rather than the part number, since a number tells you nothing when you are under the car. This matters most on mixed systems, where an exhaust pipe section from one source meets hardware from another and the two were never designed around the same flange.
Keep what is single-use, joint-specific and hard to source quickly: crush gaskets for flanges you own, clamps in the sizes your joints use, and the small clips and spacers that hold exhaust hardware in place. Keep them sealed, labelled and dry.
Do not keep used crush gaskets, clamps that have lost their shape, or anything you cannot identify. The decision rule is simple: if you would not fit it to your own car on a Sunday evening with no alternative, it does not belong in the box.