at resort - no (unless they are 18 or 19 and you have a room in their name) - only the "owner" of the reservation needs ID and needs to be present (if you have free dining then all your party needs to present at check-in)
airport - yes, they will need ID. I don't know at what age they start requiring PHOTO ID, but most kids should have some form of photo ID by that time.
On our trip two weeks ago, ds17 was never asked for ID (he does have one though). Not at airport or hotel. When I asked at the airline counter, was told sometimes TSA agents ask, sometimes they don't, depends on the agent.
At the airport they don't need to show id until they are legal age (18). However my daughter who is 17 frequently travels by herself and always carries id because looking at her most people think she is 20 or 21.
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