Yes, some people are born with different colored eyes. Medically, it called heterochromia. Most cases of heterochromia are hereditary, caused by a disease or syndrome, or due to an injury. Sometimes one eye may change color following certain diseases or injuries. Some celebrities are also heterochromia. Wentworth Miller from "Prison Break" one eye is blue and the other is green. Jane Seymour has one brown eye and one green eye.
Well, most people in the world have the same eyes color. However, everything has exceptions. As far as I know, so many half-breeds have different color eyes. For example, Wentworth Earl Miller III ,the hero of Prison Break His left eye is hazel, right eye is palegreen. Because eye color is genetically determined, so if you have a different color eyes, congratulations! You are luckier than most people in the world.