If a real eastate agent shows you houses for a long time and then you find a for sale by owner should you still pay the real estate agent and how much?

From a legal standpoint, it will depend on whether you signed a Buyer Agency Agreement and what its terms are. In general, though, it's up to your conscience or, if you prefer, sense of fair play. A Buyer Agent doesn't have to show you a house that you want to buy. He/she simply hopes/expects that you'll get him/her to prepare, present, and negotiate an offer on your behalf.