Rugby originated in the UK, with the first official written rules coming from Rugby School in 1870. It was a major influence on the creation of American, Canadian, and Australian football.
Soccer is by far the most popular sport in the world. The name comes from the "soc" in "Association Football," and was originally used to distinguish between this and rugby.
Australian Rules Football has similarities to both Rugby and Soccer, but a unique style all it's own. Due to it's fast pace, high scoring, and physical nature, it is gaining popularity around the world.