I downloaded the latest JRE 6 Update 3 as it fixed some security issues. For details, please refer to the following links:
Java Runtime Environment (JRE) Bugs Let Remote Users Bypass Network Access Restrictions
Java Web Start Bugs Let Remote Users Read/Write Files on the Target User's System
Java Runtime Environment (JRE) Lets Remote Applets Obscure the Untrusted Applet Warning Banner Display
During installation, I found that the update is trying to contact Sun. Please see the screen capture below. This is really intrusive. Anyway, I answered No and the installation was completed successfully.