You need it theoretically after the 3rd workday and could be an obstacle to some things like
- getting work
- getting (as Russian) Health Care paid
- opening a bank account
- buy a SIM Card
- paying tax
It's unbelievable hard to get a proper registration. And even I, who goes through considerable pain to pay his Russian tax (another story), gave it meanwhile up to hunt for a registration.
As that the wide (100%) majority of Russians have a low (0%) interest in paying tax nobody of the Russians I know has a registration in Moscow (except the few born in Moscow).
At the first sight the registration stuff seems to make no sense. However, it's a good reason for the police demanding pocket money from you and some hotels make money with it.
I assume also a bit, that it's serves the Russian soul as that we have an other overregulated law more in a country where they are not even able & willing to enforce the basic traffic rules (like traffic lights and speed).
Also I suspects it serves some ostrich mentality in the administration, something like '...when we have just 12 millions registrations in Moscow, we just have 12 million inhabitants, despite that gas and water consumptions doubled the last years'.
So, a registration is something very Russian. And even sometimes I have one, usually I don't.
Where I usually make a registration, is when I stay in a Russian hotel. They have to make you one... theoretically
So, yesterday I went to the town of Saransk. Not really an airport there, so an 11h night train there and back. For a quick shower before I visited my clients I checked in a hotel.
The wired thing now, was that the hotel refused to take me. They said they don't take me as guest, as that I don't have a registration.
Means the institution who is obliged to give you an registration (and is about to make 100$ for renting me an apartment for 60 min refuses) refused you due to exactly this registration.
And I don't even wanted one. I just wanted to have a shower.
This is Russian province. Actually I had once similar problems when a storm grounded my plane somewhere at the Volga. After I had to land there in the middle of the nights, the boondocks started complaining about the registration when I tried to depart. (Altogehter also an very interesting story what happened all in this night).
Sometimes in the Russian province they are still living more in USSR than in Russia, a foreigner is a thread and reported to the local FSB and all together it's a load of crap.
Friend of me once tried to make his registration (as he should do) somewhere in Sibiria. He ended up with thorax X-Ray :). And my first registration in SPB leaded to an HIV test in an building I didn't even identify in this time as hospital :)
Так... anyway, I sneaked around the problem and got my shower.
Just keep on smiling :)
Sometimes I think Russia is a collection of artificial problems and flexible solutions. This is fun (or frustration) for us foreigner and (in my opinion) the reason they can't transform there wealth in resources, culture and intellect into financial wealth for wide areas of the population.