It depends on what dog food you would give him when training. In some cases, the treats would be more healthier for the dog (but that would only happen if the dog food was a really low end type of food). Some people set aside 1/4 of the dog's regular food to use as a training treat.

You can always buy low fat treats or use carrots (as suggested). Cheese is okay but there's fat in there. You can also make your own low calorie treats and cut them up into very very small pieces. When I use treats, I cut them up into very tiny pieces. Probably the size of half of my pinky nail.

I'm not sure about the cat treats though..