A really helpful introduction to the parables of Jesus which makes an attempt to classify and explain their different styles is the Frontline site. Madeline Boucher is the chief writer (there are links to others) and the work is well organised and accessible.
Fr Felix Just’s site (as well as providing another short definition and useful explanation) has a colour chart of where the parables occur in each of the gospels. A further brief introduction is provided by English New Testament scholar Mark Goodacre.
Here is a list of the parables organised according to topic.
What is Jesus trying to do when he tells his parables?
Maybe he's inviting us to think:
Using a reasonably familiar parable like the Good Samaritan and in groups of six, invite each student to identify with a particular character in Jesus' story: the traveller, the robbers, the priest, the Levite, the Samaritan, the inn-keeper and respond to the questions above as each of them might. At the end suggest they respond as themselves.
There are a couple of other articles, more academic in tone, which teachers?senior students might also find interesting.
Letting parables live discusses the distinction between understanding the parables as allegories and the temptation to ‘allegorise’ them, that is to ascribe to them a single definitive meaning.
Interpreting Parables also warns against treating parables as allegories with set meanings and includes a very brief history of the interpretation of the gospel parables.
Parables and their social context takes a look at the First Century society in which the parables of Jesus were set. It includes a section on 'Honour and Shame' which contributes to an understanding of society and teaching in NT times.