What different acts do Catholic priests require of people who go to confession? I understand that when people go to confessional in the Catholic Church, the priest will often prescribe certain things for them to do for penance in order for their sins to be forgiven.

I have heard people in passing mention doing "Hail Mary's", and I'm pretty sure they weren't talking about long desperation passes at the end of a football game.  I've also heard mention of "Our Father's".  I assume these refer to a prayer to Mary and recitation of the Lord's Prayer.  

So, are these the most common thing a priest will prescribe?  Are there any others?  Fasting?  Is there a set pattern prescribed by the Catholic Church?
99% of the time that seems to be the case, even for mortal sins.  I've had a few "take your wife on a dates" but the most prayers I've ever been assigned was a Rosary. Generally it's just a few Hail Mary's.  I think there's a recent historical precedent for this practice, but I don't know off hand what it is, hopefully someone can expand on that.   I've heard of some pretty awesome penances in the Middle Ages and Renaissance.  

One thing that I think is required is restitution, if possible, of stolen goods.  I'm not certain if that's in some rubric or just a teaching, but to be truly penitent it would be assumed that you'd be resolved to try and make good and you usually see that in an examination of conscience following the 10 commandments under the "thou shalt not steal" section.