traveling for 4 years with kids on various airlines and speaking ime... you're always allowed to check a car seat and stroller for a lap child, as well as bring a diaper bag onboard (besides for your carryon). whats allowed to be gate checked, and what other luggage theyre entitled to, varies by arline and domestic/international. any car seat that's worth it's name will have no problem getting banged around with the checked bags. the lining of the seat, though, may get wet (if it's raining) or possibly dirty, etc. ymmv, though in many many flights, the problems i've had have been rare. strollers on most airlines you can get it gate checked in which case i think there's rarely a problem. regular checked strollers i don't have much experience with, but my guess is that if it's a sturdy stroller there shouldn't be any problems. again, the lining of the stroller might get wet, dirty, etc.