If your photo is on someones website without your perrmission, you can ask them if they would like to purchase rights to use it for a certain amount of time, or demand they take it down. You dont need to persuade them to take your photo down they stole... If they refuse, sue them.
If your picture is registered with the copyright office, and they use it without your permission, you are looking at a 6 figure law suit.
The picture is your property as soon as you press the shutter on the camera, and should not be taken lightly.
I would approach the situations the first way i stated, tell them if they would like to continue to use it, they can lease it from you... for example $500 for 5 years... Thats $100 bucks a year.
A great way to let people know its your image is to place your copyright in the photos metadata. This can be done on most adobe photo programs, I am not sure about others.