If you plan on extending your stay in Russia you need to make arrangements in advance, including the information about where you will be staying - so that can be added to your visa submission.

I think you would find getting a hotel on the spot might be very difficult - and typically visas are issued only for the exact days of your scheduled trip.

Thanks for the response. I probably wasn't clear on my question. We don't intend to extend our stay. We intend to leave Russia as soon as our cruise is finished. However, it is not uncommon to have delayed or cancelled flights on any trip. I am concerned about the cruise line's apparent refusal to extend our "invitation" for a day or two (at least) beyond our cruise ending date, to allow us to get a visa with an exit date at least two or three days after the cruise is completed. This would allow us to leave Russia without difficulty in case of any unavoidable (and likely) travel delays. I am interested in hearing other travelers' thoughts on whether this is normal practice or not. It seems silly to travel to Russia with a visa that expires the day I am expected to leave the country and I don't understand why the cruise line is insisting on this.

"I am concerned about the cruise line's apparent refusal to extend our "invitation" for a day or two (at least) beyond our cruise ending date, to allow us to get a visa with an exit date at least two or three days after the cruise is completed."

It is my understanding that is the way it has to be.

You don't get a Russian visa w/ different dates 'just in case'.

If the delay is due to a cancelled flight and your visa expires in the meantime, I don't believe you will have an issue leaving Russia although there may be a cost BUT you must double check this with the cruise company's visa company for the current rules. The issue usually occurs when a person overstays their visa because they feel like staying longer or some other reason, in this situation obtaining an emergency exit visa can take several days and cost $$$, in the meantime a visitor cannot leave Russia. Best to check with the professional visa agents as Russian visa rules are notorious for changing very frequently and without notice.

I wonder what does happen if there is some unexpected departure delay and you have to stay in Russia a day or 2 passed the expiration date. We're taking a riverboat cruise there in May, so I'm very interested in how something like that is handled.

I have heard there is an official at every International airport who can extend your visa should it be necessary due to a flight delay.
If you are delayed for another reason you could face a fine and a difficult time from Russian Immigration officials.

Russia is notorious for double checking visas for everyone tourist both entering and leaving the country. If the problem is truly a cancelled flight at the airport and the airline makes other arrangements I'm sure they would help you sort out the necessary paperwork - but do expect that to happen - and for it to be time-consuming. I've been 3 times and never had a plane cancelled. And I would assume that - barring truly awful weather - that flights are not routinely cancelled.

If you overstay your visa for another reason it is not as simple as a fine and a hard time from immigration, another visa must be issued to get out of the country. There is no such thing as extending a visa, it is a new visa, an exit visa.

I think you are getting bad advice.
It is an excellent idea to get a visa covering slightly before and several days or more after expected exit dates.
The problem is likely that the sales agency is using a visa support service and it not getting the request straight. If they are not registered as a hotel or Russian tour operator, they have to apply to one of those for the invitation(called Visa Support). I am an American living in St Petersburg and deal with many visitors every year concerning visas, and have federal registration to issue invitations so this is something I know about and and how the immigration officials view overstays. The reason for an overstay is not important.
The problem might be that you are not dealing with the river boat operators and using a sales agent. Sales agents usually o not have access to visa support directly themselves so they subcontract that. Either approach the boat company directly in Russia or get your own visa support for up to 30 days through any of hundreds of companies who resell visa support documents. It ought to be $20-30 for a 30 day visa and include any members of the family traveling together on the same document. Most visa agencies who resell the documents charge for each member of the group traveling together which is a rip off since the consulate wants up to 5 passports listed per Visa Support document.
Getting that raises another problem, you can't apply for a tourist visa until within 45 days of arrival. After getting the visa support document, apply for the visa. If you are applying in Europe, other than the UK, you can apply to your nearest consulate directly. UK citizens will have to go through a visa application center to be the middle man, who actually turns in the application for an additional charge.
You will need a visa or passport style photo, the consular fee, your passport, the visa support document, and a completed application form. The application form is filled out on-line at http://evisa.kdmid.ru/ and then print the resulting document as your completed application form. You will receive a visa pasted into your passport taking up 1 fullpage. Another empty page is needed for entry and exit stamps.
Since you have so far to get the visa, why not stay a few more days to explore on your own. Rent an apartment for $80-100 or so a day and relax while exploring at your own pace if you are ending your cruise in St Petersburg. If ending in Moscow, hotels and apartments are more expensive and not quite as tourist friendly.
Some companies who book river cruises can host foreign guests and provide private tours and activities without all the middlemen and markups.
If you have any specific questions let me know. Which boat are you booked on?

Am Expat - thanks so much for taking the time to provide all your thoughts. What you have advised is in line with the research I have done.

We are taking a Viking river cruise from Moscow to St. P next May (2013). I have contacted our travel agent, Viking directly and their visa service and all 3 are telling me the same thing - that the visa exp. date will be the date the cruise ends. I am beginning to think the problem is that Viking doesn't want to be "responsible" for us for any extra days, and so would rather that their passengers assume all the risks associated with any travel delays.

However, since we have booked our flights thru Viking, I can't see where they are really assuming any extra risk that we will stay extra days in Russia and cause some type of trouble that Viking would be held responsible for if they gave us a few extra days on the "invitation." My goal in seeking info from those of you with experience in this area is to see if I was correct before I start to make a real issue of this with my travel agent and Viking...which I now intend to do.

I can't believe other Viking cruise travelers are willing to just meekly go along with these arrangements!

I don;t see why they won't extend you visa - but I think you will have to book hotels for those nights for them to do so.