Airlines have been pretty generous with allowing playpens, strollers, car seats and luggage to be checked in but this is tightening up. There is still a free luggage allowance for infants, but it is quickly becoming a policy where one item can be checked in for free and the rest either is left behind, or you use up some of your own free baggage allowance to transport items like a stroller or a car seat.
Airlines are also tightening up on the stroller issue. Larger strollers are increasingly required check in at the check in counter and not at the gate. Part of this is the sheer size of some strollers can make it difficult for ramp agents to get them stowed quickly and safely. If your stroller is weighing more than about 15lbs or 7kg, you may be asked to check it in before going to the gate area.
What You Can Pack for an Infant
Strollers and the Gate
image courtesy of Arlene Fleming