I flew overseas with ours and checked it in and it was no problem. I know they will let you gate check a stroller or car seat but I don't know about a Pack N Play. It's probably too big to carry on I would think.
I fly between the midwest to visit my home/family on the east coast frequently and have always checked my portable crib. However the last time we flew they limited how many bags I could check and we had to carry the stroller and crib as a carry on that the flight attendants stowed once we boarded the plane. I havent flown since the majority of airlines are charging for baggage now so you may want to check on any additional costs.
Thanks for all your great replies! I called the hotels and inns ahead of time, asking them if their cribs were Pack 'N Plays, and sure enough they were. So we ended up not bringing our own and just using those in the hotel. One Pack 'N Play was an older model, though, so the fitted sheets we brought along were too small. We just used a regular top sheet, folded it many times, and tucked the edges under the Pack 'N Play mattress. My daughter slept in it as well as would be expected for a baby in a new environment. Thank you all again!