I once heard someone say that a parable was an "eartlhy story with a heavenly meaning." That sounds pretty, right? But it doesn't quite answer why Jesus used them. They aren't always the easiest lessons to understand (heck, they even left his Disciples baffled). So what's the point?
First off, while parables today are a bit obsolete, back in Jesus day they probably would have been more viral then a Justin Bieber video--at least in Judaism, where they were pretty common place.
I can only give you my own rational why Jesus used them: to separate the devoted from the casual listener. Spiritually speaking there are two kinds of people; the first person is the one who finds the idea of God pretty remarkable--they're willing to believe it, but they aren't willing to be fruitful with it; they want to go to church on Sunday, take a little nap, then go home and go on living; the idea of taking something out of the sermon is nice--as long as they don't have to work for it. The second kind of person, is the one who truly wants to grow; they're willing to take something that's hard to see and think about it--to let God reveal something in their life.
Think of the last truly profound movie you saw; you walked out of the theater really thinking about what the director was trying to convey on screen, and then you look around--chances are there's at least one person shaking their head saying, "Well that was stupid." That's how I imagine these parables. People either walked away thinking about what was said, and then there's going to be another group of people say, "I don't know what all the fuss is about." There was probably also a third group who walked away pretending to think it was profound just so they'd fit in.
Ultimately, I believe he spoke parables to provoke discussion--to get people to say, "What do you think he meant?"
If you want to read all of the Parables of Jesus, there is a list below. There are 36 total. There are also a several parables not in the Bible--some might be real, others are not.
The Growing Seed (Mark 4:26-29)
The Two Debtors (Luke 7:41-43)
The Lamp under a Bushel (Matthew 5:14-15, Mark 4:21-25, Luke 8:16-18)
Parable of the Good Samaritan (Luke 10:30-37)
The Friend at Night (Luke 11:5-8)
The Rich Fool (Luke 12:16-21)
The Wise and the Foolish Builders (Matthew 7:24-27, Luke 6:46-49)
New Wine into Old Wineskins (Matthew 9:17-17, Mark 2:22-22, Luke 5:37-39)
Parable of the strong man (Matthew 12:29-29, Mark 3:27-27, Luke 11:21-22)
Parable of the Sower (Matthew 13:3-9, Mark 4:3-9, Luke 8:5-8)
The Tares (Matthew 13:24-30)
The Barren Fig Tree (Luke 13:6-9)
Parable of the Mustard Seed (Matthew 13:31-32, Mark 4:30-32, Luke 13:18-19)
The Leaven (Matthew 13:33-33, Luke 13:20-21)
Parable of the Pearl (Matthew 13:44-46)
Drawing in the Net (Matthew 13:47-50)
The Hidden Treasure (Matthew 13:52-52)
Counting the Cost (Luke 14:28-33)
The Lost Sheep (Matthew 18:10-14, Luke 15:4-6)
The Unforgiving Servant (Matthew 18:23-35)
The Lost Coin (Luke 15:8-9)
Parable of the Prodigal Son (Luke 15:11-32)
The Unjust Steward (Luke 16:1-13)
Rich man and Lazarus (Luke 16:19-31)
The Master and Servant (Luke 17:7-10)
The Unjust Judge (Luke 18:1-9)
Pharisees and the Publican (Luke 18:10-14)
The Workers in the Vineyard (Matthew 20:1-16)
The Two Sons (Matthew 21:28-32)
The Wicked Husbandmen (Matthew 21:33-41, Mark 12:1-9, Luke 20:9-16)
The Great Banquet (Matthew 22:1-14, Luke 14:16-24)
The Budding Fig Tree Matthew 24:32-35, Mark 13:28-31, Luke 21:29-33)
The Faithful Servant (Matthew 24:42-51, Mark 13:34-37, Luke 12:35-48)
The Ten Virgins (Matthew 25:1-13)
The Talents or Minas (Matthew 25:14-30, Luke 19:12-27)
The Sheep and the Goats (Matthew 25:31-46)