Genesis 1:26 says "Then God said, 'Let us make man in our image, in our likeness. and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground.'"
Some people have an odd idea about what it means to "rule over" something or someone. For many these words connotate the act of dominating and controlling something or someone without any responsibility as to the welfare of the person, animal or object (in the case of humans or animals this includes their psychological welfare as well). This sort of domination can be very destructive.
As Gods representative, we are to rule over things in the same manner that he rules over things. He is our example. He cares for the plants and animals of the earth. He cares for us. He gives us the things we need in good measure. He gives us just enough to sustain us (fairly comfortably for most of us) while at the same time keeping us in a position where we have enough stress to encourage growth.
God is not greedy with us. He does not demand our all without his giving anything in return. Though he can be harsh with us at times he does not abuse us or use us in a selfish way without this benifiting us in some way. There is always a return.
Remember the example of Jesus, he was like a servant in that he fostered the growth of those around him.
As God's representatives here on earth we are to "rule over" the bits of this world that he has given us specifically to rule over. Things like our houses, cars, children, animals, local parks, and highways. As God's representatives here on earth we are to rule over these things in the way that God rules over us and the rest of his creation. God is a steward, he cares for things, we are God's representatives, we are stewards over what he has given us to be stewards over.