There are several implementations of Java. The three most common implementations when talking about it for Ubuntu are:

• OpenJDK: The primary goal of the OpenJDK project is to produce an
  open-source implementation of the Java SE Platform (6 and 7). This is
  the default version of Java that Ubuntu uses and is the easiest to
  install.


• Sun Java: Sun Java is the reference implementation for Java 6. Its support has been discontinued in Ubuntu.


• Oracle Java: Oracle Java is the OpenJDK Java Se Platform version 7 implementation from Oracle. Oracle introduced with this implementation a license that prevents distribution.

Since Ubuntu 11.10 (Oneiric Ocelot) and due to license issues Ubuntu will no longer distribute Oracle's JDK and JRE. Also, previous versions supplied on PPAs suffer from security issues and are not recommended to be installed on any Ubuntu system.

There are no more supported .deb releases from Ubuntu with reference to Sun Java or Oracle Java, Ubuntu officially supports OpenJDK and OpenJRE implementation of Java which is the base for Oracle's own implementation.

OpenJRE is the official implementation of Java Runtime Environment (JRE) for your Ubuntu systems and should suffice to run any Java program that you might require and it's included in the main repository and it's easily installable.

OpenJRE

By opening a terminal and typing

sudo apt-get install default-jre

this installs openjdk-11-jre (at the time of writing this, you may install a newer java version in the future, which is now, if it installs a different openjdk version I guess)

The openjdk-11-jre package contains just the Java Runtime Environment. If you want to develop Java programs then install the default-jdk package:

Also important is to install the wrapper for supporting Java applications on your web browser, the Iced-Tea Java Plugin.

IcedTea Plugin

Or via a terminal

sudo apt-get install icedtea-plugin

Or look for icedtea-plugin in the Ubuntu Software Center.

To make sure that you are running the correct version of Java, use this command to set your choice:

sudo update-alternatives --config java

java -version should display the choice you previously made.

If you need to install OpenJDK-JRE 6 or OpenJDK-JDK 6

openjdk-6-jre (click to install) is available for installation for Ubuntu 8.04 (Hardy Heron) and up.

Install it with

sudo apt-get install openjdk-6-jre

Or if you need the developers' package, openjdk-6-jdk (click to install), install it with:

sudo apt-get install openjdk-6-jdk

A version of the icedtea-plugin (click to install) is also available to install if you are going to use OpenJDK 6.

Install it with:

sudo apt-get install icedtea6-plugin

If you really want to use Oracle's Java SE Platform, see How can I install Sun/Oracle's proprietary Java JDK 6/7/8 or JRE?.