Actually, it depends…
If you are talking about just what is needed for casual browsing where Java applets might show, then you can probably get rid of everything up to Java 6.
However, developers do have the ability to specify which version of the JRE is used with their apps, so there are sometimes cases where you would need older ones present on a machine. I am willing to bet that this is for more intense things than the casual surfer is liable to encounter.
For example, we have some internal applications that run against WebLogic 8.1, and these apps are stuck in Java 1.4 since the server side WebLogic engine runs on Java 1.4 and a lot of the internals related to the network communications needed for WLS changed radically between 1.4 and 1.5.
On a modern machine, it can’t hurt to keep around all of the JREs. They don’t take up much disk space.