I realise that this question is subject to local trends (and I'm in the US), but I encourage people in other countries to submit their methods!
How do you accept packages/deliveries anonymously? Of course, there are mail redirection services, but a third party which corroborates with different parts of the chain can likely figure out your identity and what you have purchased/have incoming.
I haven't been able to find a good solution to this yet, and I believe the new rule in the US is that the receivers identity must be reported to the government? This (or a variation of this, I don't remember) is a recent event.
Depends on what you want delivered and your threat model:
There are services that will buy stuff from Amazon have it delivered to a locker and they give you the code: https://anonshop.app/
For mail one method has been to scout out a house, the have mail sent to it. Pick it up from the house. (Nobody home, before owners retrieve it, etc) - this is illegal and considered theft of mail
You can pay someone money to receive a package then they can leave it at a dead drop
You can get have someone else setup a mailbox for you, but give you the key. (Post box, or mailbox etc)
You can use a virtual address service, and they receive the mail for you and scan it so you don't need physical delivery.
If your just going for general privacy any method is fine.
If you want to accept packages from fans but not give out your home address and PO box works
If you want to something that can get you in trouble you have to now account for whoever is going to get you into trouble and how much effort they will put into finding you, and what 'rules' they will follow.
Trackers In a package - Faraday cage..
Watching the mailbox to see who picks it up - don't pick up consistently/counter surveillance
Packages that explode, or poisoned - examine, scan, open in controlled environment.
If your adversary is the mail system, do something else. They can scan all packed for patterns, check for chemicals, x-ray, density scan, etc. if your trying to hide from the network (mail system) while using them systematically your going to lose.
For mail one method has been to scout out a house, the have mail sent to it. Pick it up from the house. (Nobody home, before owners retrieve it, etc) - this is illegal and considered theft of mail
An empty plot might be a better idea, I had an acquittance who installed a mailbox in an empty plot on his neighbourhood and had stuff sent there.
I've heard one criticism of this method which is that mail carriers generally know which houses are vacant, so if they get a suspicious package going to such an address that may actually raise an alarm.
For people ordering drugs for example people will recommend using USPS and a real person's name/address, since the US postal service requires a warrant before inspecting a package, and the idea is you're trying to hide in plain sight.