There is as much confusion and rumor about how to get a visa or register as there is with any other topic concerning Russia. Actually the rules are not so complicated, and the Internet suggestions primarily concern trying to skirt the laws rather than to comply with the pretty straight forward procedures.
The laws changed last year to bring Russian tourism up to a more professional level. All reference numbers held in the past were cancelled by June 1st 2007 and new Unified Federal Registration was adopted with a new numbering system for hotels and tour operators who demonstrated financial responsibility by posting a 10,000,000 Ruble(about $420,000) into a fund from which claims from visitors who were cheated or not properly accommodated and to receive compensation. The majority of prior reference number holder did not apply for new authorization. Here in St Petersburg, there were approximately 1200 such reference numbers before June 1st and about 380 currently. This law more closely aligned tourism practices in Russia to Europe and North America.
New reference numbers called MBT numbers were assigned to the complying tour operators and hotels. To invite and sponsor a foreign visitor, this number if required. A different, lower requirement is needed for tour and hotel operators who host Russian tourism in-country or outbound.
Visa services do not have this right of sponsorship or invitation so they buy visa support from willing hotel clerks or others wanting to risk their employment. That is why visa support documents supplied from visa services are never for the hotels or tour operators you are actually using.. The new law shifts the responsibility of compliance to the host and away from the visitor. Gone are the fines for not registering, which used to have a maximum penalty of 600 Rubles.
The sponsor, usually hotel or tour operator is now responsible for registering their guest and again reporting shortly after the visitor has departed the country by turning in the original registration application. The visitor has no action required of them, or cost in theory. But recently less than ethical hotels and tour operators have been adding registration fees. So for visitors, the whole process is invisible to them. They need not carry proof of registration, a photocopy of a slice of the registration application is enough to show it was applied for.
For those not registering with their sponsor, selected post offices and OVIR can do it. Post offices are preferred, they usually have shorter lines.
Visitors are often asked who their sponsor is nowadays because it is important. A regular hotel or tour operator will have their name and their MBT number on your VISA support documents, and they will match. Visa services usually do not tell their customers what hotel is "sponsoring" the client. It is on your visa so be sure to know. That hotel is responsible for registration if you go there, and if you do not know who sponsored you the immigration officer can on their own discretion, deny your entry.
Here is a link to ALL the currently issued MBT numbers from the official government site:
http://www.russiatourism.ru/section_5/ it is in Russian, and the file needed for international tourism is reached by clicking on the link labeled: Международный туризм
It is a MS Word 2003 Document.
If your tour operator is not on the list, you are not getting the whole story.
Overall, tourist visas and registration is easier than ever for the vast majority of visitors who get the correct visa for their type of visit, most ethical hotels or tour operators send visa support for free, and once in the country, registration is a free and invisible requirement for the visitor, and exiting has lost the worry about not being properly registered.
There are bigger changes with the Business Visa but that is for another post if anyone is interested.