What battles did King Arthur fight?

If you're talking about the real life King Arthur, the only battle that people can decide conclusively that he fought in was the Battle of Badon Hill, where he defeated the Saxons. The battle at the end of the King Arthur film from 2004 is based on that battle.

However, we really don't know that much about Arthur from history, as there isn't much archeology supporting his existence. Most scholars don't even think he was a king, but rather a war leader who brought peace to his area for close to half a century.

If you were talking about the fantasy Arthur, then I can't really help you.