When is passport stamped?

You passport is stamped when you enter or leave a country, to record that you legally entered the country, and how long you are allowed to stay, so the authorities can check you are legally in the country.
The Russians will stamp your passport when you arrive in St. Petersburg. In Helsinki airport you will stay "airside", you will not legally enter Finland so your passport will not be stamped by the Finns. If you exit the airport (stay overnight in Helsinki), then your passport will be stamped for entering and exiting Finland.

Usually countries only stamp foreign passports, they do not stamp the passports of their own citizens as they can come and go as they wish.

Usually countries only stamp foreign passports, they do not stamp the
passports of their own citizens as they can come and go as they wish.

Before I got Global Entry 2-3 years ago, my passport was always stamped when I returned to the US (a blue stamp too) regardless of whether that were at JFK, BOS, ATL or DTW. US Immigration may still do it?

Continental, the US is, as is often the case, the exception to the rule.
Also, some countries do not stamp on exit, only on entry, even for foreigners. This is the case with the UK. There is no passport check on exit from the UK, but the airlines have to, by law, give the passenger list to the government. This causes problems with Eurostar, as trains don't have ID checks. So Eurostar has to employ extra people at St Pancras to check ID before you get on the train and record the details.

Continental: entering the US, one's passport is no longer stamped (with or without Global Entry). I'm not sure when it changed, but you're right - until around a few years ago, everyone (US citizens included) got a stamp in their passport when entering the US. Conversely, the US is one of those few countries, like the UK, where there is no passport control on exit

Andrea: you now have your answer for this trip. But for future trips, you should know about the Schengen zone. This is a group of European countries that have agreed to abolish routine border checks. You go through passport control and get stamped at your first entry into the zone; all other travel in the zone does not have passport control. So, for instance, if you were flying New York to Helsinki to Warsaw or Berlin, you'd get your passport stamped in Helsinki.

Point of confusion: Norway and Switzerland and Iceland are not in the EU, but are in Schengen. The Ireland and (for now) the UK are in the EU, but not in Schengen. So, if you fly New York via London or Dublin to Berlin, you'd stay airside (as you will for your trip via Helsinki to St. Petersburg), and only get your passport stamped in Berlin.

I don't think it's the case that the United States has always consistently stamped the passports of US citizens at airport ports of entry, even more than a couple of years ago. From the mid-1990s to the mid-2000s (US citizen) I always entered the US at LAX and never once received a stamp in my US passport. Since then, I have cleared US passport control in Chicago, New York, Miami, Boston, Vancouver, Toronto and Montreal and have had a very inconsistent passport stamping record, even at the same airport.

"like the UK, where there is no passport control on exit"

Whilst UK airports don't have an uniformed official in a glass booth checking your passport, in the way you find in other countries here, there are exit records kept. It just happens electronically "behind the scenes" as part of other passport checks; so you may not realise it has happened. That's the theory, anyway. Last year the UK government department responsible found it had exit confirmations for 200,000 foreigners it didn't know had ever arrived and also was missing 600,000 official departure records for people it thought had gone.

Pertaining to the US, I'll bring up my experience upon re-entry at SFO or OAK. Until a couple of years ago, my US passport was always stamped as a matter of course before I was finished with Immigration.

Now, when I am finished, my passport is closed and that's it. No stamp. At that point I ask for the stamp. They have always obliged me when I've asked. . So, every Europe trip at re-entry at SFO or OAK has gotten a stamp.

Bottom line, if you have an US passport and want a stamp at re-entry, just ask, it will be stamped.

If it means anything, when I cleared US CBP at Dublin in September 2016 my passport was not stamped, but, clearing at Dulles in September 2017 it was stamped.

I was on RS Europe trip in 2015. France, Germany, Switzerland and Italy. Our guide mentioned that we could get a hand stamp in Switzerland if we wanted it. My passport has no stamps in it at all and a tour member asked how that happened. It was my first time overseas so I have no idea why no one stamped my passport. I was told that if I needed to prove that I had been cleared to be in any of those countries, I needed the stamp. I never had to prove.