I saw people with their own at Typhoon Lagoon. We rented one. It is a free rental but you have to leave an ID card to ensure you return it. My wife waited in line to get one and didn't have a drivers license with her so she had to leave the room key. Luckily I had one too or we wouldn't have been able to charge our meal and we didn't have much cash with us. You also have to wait in line at the end of the day to return it. Kind of a pain. If you are driving and space isn't a problem I would take it. If flying I wouldn't mess with it.
You can also rent towels for $1 at TL. They are free at resort.