I went to see a rental home and the landlord made a verbal agreeent to rent it to me and the next morning rent it to someone else. Can I sue them for this?

You can, but will probably lose, because the landlord could just say that he had made it conditional on a credit/reference check or some such, which would be typical, so the judge will most likely believe him. I assume that you hadn't written a check..

Also, you would have to show that you suffered damages as a result of the switch. Don't waste your time or the courts with this.