They always have some code to make traceability possible, but whether it is a SN (or equivalent, such as a VIN), a manufacturing date, expiration date or batch number will depend on the nature of the product. Sometimes the numbers themselves codify information: some poultry coops stamp every individual egg with a code including when was it laid, what farm it comes from… it’s not a serial number, but again it’s about traceablity.
[soap box]
Traceability has different benefits for different parties; they’re mostly related to quality control, process improvements (not only in Production, but also in Logistics, Quality or Maintenance), maintenance and logistics.
Logistics: one of the advantages of traceability is that, by having a shipment number and some way to interact with the shipper’s computers (person to person contact or web-based), both the recipient and the sender can find out where the item is at any given time. It isn’t a matter of “ship it and it will arrive whenever it does”, as it used to be.
Quality: tracking what went into making a problematic item, when was it made, by whom, using what machines. If you discover that one of your components is bad, you can find out which produced batches/series it affected and act accordingly (analyze what you still have in storage, recall product, contact your clients to warn them of the issue and provide a fix…)
Process improvement: since you can analyze all the information about when, how and with what was an item made, you can get a better view of the causes and hopefully improve the process to avoid reoccurrence. Depending on what the cause was, the process that needs to be improved may not be a Production one: you may need to control certain products more often (for example, runs under one day get inspected once, longer runs get inspected once-a-day instead of only once), or to clean the machines better (literal quote: “how many times have I told you that when you drop copper sulfate on the scale it has to be cleaned yesterday!”). You may also find out that the wrong truck was used (food-container instead of chemicals-container comes to mind), or that a product clearly labeled “protect from sunlight” spent three months sitting in a yard under the tropical sun: yep, it grew colonies and I don’t mean the kind that smell well.
Maintenance: only people with serious anatomical problems worry about which individual monkey wrench was used to close a valve, but the valve itself can cost anywhere from a few cents to six figures. When your valves cost more than three times your salary, you kind of want to be able to track when any of them was bought, when was it installed, when was it cleaned, whether any of them has been refitted, that one was removed from location A then refitted then installed in location B… It can help you do things such as convince your boss that it really is worth it to buy the ones that cost 150K and last 2 years rather than the ones which only cost 60K but last 3 months (yes, that is a real example).
I could go on for hours but I don’t want to bore you more. My area of expertise (that sounds so posh) is Operations: Production, Quality, Maintenance (both internal and for customers), a bit of EHS… so I work with and for people who often need to be convinced that they really, really, really do not need to track this or that detail specifically (the computer will do it for them, yes I love redundancy too but seriously, in this case it’s additional work for no additional safety or security. Cross my heart).