As others have stated, there were two monarchs that ruled during Shakespeare's life, which was roughly from 1564-1616. I will try to add new insight into these two characters, as opposed to repeating what other answers have already stated.
1. Elizabeth the First (reigned from 1558 to 1603)
Elizabeth the First is one of the most famous rulers in the history of England. It was uncertain that she was going to rule, and many English people (particularly Roman Catholics) found Elizabeth to be an illegitimate ruler. She is famous for many things, including her extreme intelligence and cunning wit. Elizabeth the First is said to have known six languages. Shakespeare's early plays have many linguistic jokes, and this could be traced to his affection for Elizabeth the First.
2. James the First (reigned from 1603 to 1625)
James the First was initially the king of Scotland, but he also became the king of England in 1603. This unification created the kingdom of Great Britain, which exists today. One of his greatest contributions as king was the creation of the Authorized King Jame's Version of the Bible, created in 1611. This has continued to be the standard bible text today. James was a peaceful king, and often tried to unify countries. Shakespeare's enthusiasm with other parts of Great Britain could be attributed to the rule of James the First.