The package sun-java6-jre is not currently installable and gives the following error:
root@raspberrypi:~# apt-get install sun-java6-jre
Reading package lists... Done
Building dependency tree      
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
sun-java6-jre : Depends: sun-java6-bin (>= 6.26-0squeeze1) but it is not installable or
                         ia32-sun-java6-bin (>= 6.26-0squeeze1) but it is not installable
E: Broken packages
So let's give openjdk a try:
root@raspberrypi:~# apt-get install openjdk-6-jdk
Reading package lists... Done
Building dependency tree      
Reading state information... Done
The following extra packages will be installed:
 ca-certificates ca-certificates-java icedtea-6-jre-cacao java-common
 libaccess-bridge-java libaccess-bridge-java-jni libasyncns0 libflac8
 libgif4 libice-dev liblcms1 libpthread-stubs0 libpthread-stubs0-dev
 libpulse0 libsm-dev libsndfile1 libvorbisenc2 libx11-dev libxau-dev
 libxcb1-dev libxdmcp-dev libxt-dev openjdk-6-jre openjdk-6-jre-headless
 openjdk-6-jre-lib openssl ttf-dejavu-extra tzdata-java x11proto-core-dev
 x11proto-input-dev x11proto-kb-dev xtrans-dev
Suggested packages:
 default-jre equivs liblcms-utils pulseaudio openjdk-6-demo openjdk-6-source
 visualvm icedtea6-plugin libnss-mdns sun-java6-fonts ttf-baekmuk
 ttf-unfonts ttf-unfonts-core ttf-sazanami-gothic ttf-kochi-gothic
 ttf-sazanami-mincho ttf-kochi-mincho ttf-wqy-microhei ttf-wqy-zenhei
 ttf-indic-fonts
The following NEW packages will be installed:
 ca-certificates ca-certificates-java icedtea-6-jre-cacao java-common
 libaccess-bridge-java libaccess-bridge-java-jni libasyncns0 libflac8
 libgif4 libice-dev liblcms1 libpthread-stubs0 libpthread-stubs0-dev
 libpulse0 libsm-dev libsndfile1 libvorbisenc2 libx11-dev libxau-dev
 libxcb1-dev libxdmcp-dev libxt-dev openjdk-6-jdk openjdk-6-jre
 openjdk-6-jre-headless openjdk-6-jre-lib openssl ttf-dejavu-extra
 tzdata-java x11proto-core-dev x11proto-input-dev x11proto-kb-dev xtrans-dev
0 upgraded, 33 newly installed, 0 to remove and 0 not upgraded.
Need to get 50.2 MB of archives.
After this operation, 139 MB of additional disk space will be used.
Do you want to continue [Y/n]? Y
Looks like it works!
root@raspberrypi:~# java -version
java version "1.6.0_18"
OpenJDK Runtime Environment (IcedTea6 1.8.13) (6b18-1.8.13-0+squeeze1)
OpenJDK Zero VM (build 14.0-b16, mixed mode)