All of the events that Bukkit provides can be found in the API documentation in the package org.bukkit.event. The Javadoc has a full list of the Bukkit events at http://jd.bukkit.org/dev/apidocs/org/bukkit/event/class-use/Event.html. I suggest you look at the list to see what type of events you can listen for. Each event has several methods which give you more information and allow you to modify it. For example, BlockBreakEvent provides methods to get the block that was broken and the player who broke it. Most events may also be canceled if you wish to not allow the event to occur. This is useful in many situations, such as not letting a new player place a TNT block or preventing a mob from spawning.
As mentioned earlier, listening to events can aid in automating your server and reducing the number of commands being sent. Besides that, they can simply be a lot of fun to work with. Let's look at a few examples of plugins that could be made using the Bukkit event system. Earlier...