Well, I took three carry-ons aboard my return flight on Aeroflot last June (SVO-ORD) and no one batted an eyelash. I had a larger carry-on - a two-wheeled F/A-type bag - and two smaller bags. They fit neatly into either the overhead bin on the 767-300ER or under the seat in front of me. Aeroflot isn't too strict about that sort of thing.
However, on other flights, I've been severely limited - in fact, not only was I allowed one carry-on only on SAS in 1996, they wanted to fine me for the additional luggage (2 boxes and a duffel bag) I had as I was moving back from living abroad after 4.5 years. Since I had no money, I ended up having to leave three items behind in Stockholm, where they are to this day.
So based on my experience, the number of carry-ons allowed depends on the airline, as well as how full the flight is, in many cases. Several airlines have strict set standards they abide by. Others, like Aeroflot, LOT, CSA and MALEV, don't.