The basic tenets of the Catholic Church have remained the same:
- The ten commandments must be obeyed
- The sacraments (7) impart grace to the soul
- The transubstantiation is real (the host becoming Christ's body and blood)
- Birth control is prohibited, as is abortion
- People who die with mortal sin upon their souls will be condemned to hell. Those with venial sins must suffer in Purgatory until they are cleansed of sin so that they may enter Heaven.
- The hierarchy of the Church remains as it has been since the establishing of Peter as the first pope
- There are certain impediments to marriage that prohibit couples from marrying in the Church
- Divorce or marriage with a divorced person is not allowed.
As the previous poster has mentioned, after Vatican II in 1963, great changes were made. In addition to what has been mentioned,
- Women have been allowed near the altar.
- Women no longer need to cover their heads.
In the 16th century, the Catholic Church had a lot of practices going on that clerics within the church were opposed to. That is why Martin Luther, who was a priest, nailed his 95 theses to the door of the cathedral in Wittenberg. If you do some research, you can find the 95 theses online and see what Martin Luther opposed - the sale of indulgences, for example, confessing to a priest instead of directly to God, etc. However, it depends on what you mean by "rules" - because the church had rules that were not necessarily being followed. Sinful men were perverting the rules and the church was accused of corruption. However, the sacrements and rules of the church remained the same and some of them are still the same.
Something that had a huge influence on changes in the modern church was a council called Vatican II. If you research this, you will see how the modern church is different today even more. For example, it used to not be OK to be cremated in the Catholic Church, but Vatican II changed that. The modern church is not required to have the mass in Latin. In many modern churches now, the priest faces the people, not the altar -- things like that. These are "practices" of the church, that is why I ask about what you mean by rules.
As far as sacrements and tenets of the church, those have remained pretty constant. There are still 7 sacrements and rules regarding them, abortion is still not OK, priests still cannot marry, but there have been changes made to confession and communion. However, Catholics still believe in many of the same things.