Right now, things at Moscow airports are pretty much normal. If I was going to fly there a week from now, I wouldn't worry too much. A month from now, all bets are off.
As long as the economic sanctions against Russia remain nominal, targeting only a few key personnel, the situation should remain normal for the rest of us. However, if Russia doesn't give in and return Crimea to Ukraine (which doesn't seem likely), some real sanctions are probably going to take place. When that happens, there may be severe restrictions for flights between Russia and EU.
Iraq did a similar thing in 1990. Because it was only a regional power, the rest of the world went to war to reverse the annexation of Kuwait. Russia is a much bigger player, so nobody is seriously considering a military intervention. Still, I would be very surprised, if the future developments did not seriously inconvenience pretty much everyone traveling to Russia for business, leisure, or transit.
I should be going to a conference in Moscow in June, but I've been delaying travel arrangements and visa application to the last possible moment. Unfortunately that last possible moment will be in a couple of weeks, and there are no signs of the situation getting resolved before that.