If you take your house off the market do you owe the estate agent any fee?

Typically no but it depends on the listing agreement you signed. Read it carefully. If the listing period has expired many listing agreements state that if a person was shown your property during the time it was listed and wants to buy it after the listing has expired you may still owe the real estate Company a commission. Most listing agreements speak to this in the agreement with a time period - like 180 day - after the listing has expired. This is the way a Real Estate Broker protects themselves from people trying to go around them by dealing directly with the seller.