The Flying Carpet is an item and mode of transportation in several Dragon Quest games, beginning with Dragon Quest V. Using it, the hero's party can travel over land and sea, but not over mountains and forests.
Dragon Quest V
The Flying Carpet can be obtained in the third act of Dragon Quest V, in the town of Lofty Peak.
Dragon Quest VI
Dragon Quest VI had two variations with the same function. First you obtain the Flying Bed, which is functionally identical to the Magic Carpet, but only works in the Dream World. The Flying Bed is obtained in Clear Vale. The carpet is obtained later on by participating in the Style Competition and winning three times. The prize is the Beautiful Carpet. To obtain the Magic Carpet the Beautiful Carpet must be taken to the magical city of Calberona, where it can be reenchanted.
Dragon Quest VII
The Magic Carpet is first mentioned in the village of Mezar. A man named Nicola lives there and dreams of giving the carpet to the Legendary Hero. When the party approaches he gives away the carpet immediately, but it won't fly. Upon returning to Mezar, Nicola takes back his carpet, saying the party aren't true adventurers and the carpet didn't choose them. It's later discovered that the maid, under orders from Nicola's late father, hid the true carpet. She agrees to give it to you when she's allowed to see the Merm Moon.