Is the Universe Flat?

Just a quick question since Columbus just discovered America after proving the world was not flat: Is the universe flat? Every picture I see shows a swirling mass of heavenly bodies all spread out in one dimension. So is it flat like that or is it more like a snow globe where you can go up and down and still find stars and stuff? If anyone has been out there or knows someone who has, please fill in this gap in my knowledge base.