12.04 LTS

The preferred method:
Open Software Center -

In Ubuntu software center select Eclipse
I installed the Extensible Tool Paltform and Java IDE as well, but installing that is optional.

Enter your password in the authentication dialog.
This will get you 3.7.1 inside of a package management system.

Alternative options:

The next most preferred method
PPA:
As of this moment, the eclipse-team PPA has no eclipse package for 12.04.
I‘ll update the answer as things develop.

When it becomes available, if you already installed via software center-
sudo add-apt-repository ppa:eclipse-team/ppa && sudo apt-get update && sudo apt-get upgrade

The least preferred method
Portable:
For a portable installation you can still download directly from the Eclipse website. This gives you the ability to customize several Eclipse installations for different languages CDT, Java, and PyDev or Aptana for instance. It doesn‘t allow automatic updates. Installing through Software Center is always the preferred method.

I tested the portable 3.7.1 and 3.7.2 tarballs and they work just fine on 12.04 LTS.

An added disadvantage to portable installs is that you have to update your launcher if you move the folder or launch it directly.

How to install Eclipse 4.2 on Ubuntu 12.04

Since the Eclipse packages in the Ubuntu repositories are out of date, if we want to install latest releases, we are going to have to do it manually. You can just download the tar.gz file from eclipse.org.

1. Download Eclipse. I got eclipse-jee-juno-SR1-linux-gtk.tar.gz

2. Extract it by executing a command line

   tar -xzf eclipse-jee-juno-SR1-linux-gtk.tar.gz
   

   Or with Archive Manager extraction.

3. Move extracted eclipse folder to /opt/ folder

   mv eclipse /opt/
   sudo chown -R root:root /opt/eclipse
   sudo chmod -R +r /opt/eclipse
   

4. Create an eclipse executable in your user path

   sudo touch /usr/bin/eclipse
   sudo chmod 755 /usr/bin/eclipse
   

   Create a file named eclipse in /usr/bin/ with your preferred editor (nano, gedit, vi...)

   Copy this into it

   #!/bin/sh    
   export ECLIPSE_HOME="/opt/eclipse"
   $ECLIPSE_HOME/eclipse $*
   

   And save the file

5. Create a Gnome menu item

   Create a file named eclipse.desktop in /usr/share/applications/ with your preferred editor (nano, gedit, vi...)

   Copy this into it

   [Desktop Entry]
   Encoding=UTF-8
   Name=Eclipse
   Comment=Eclipse IDE
   Exec=eclipse
   Icon=/opt/eclipse/icon.xpm
   Terminal=false
   Type=Application
   Categories=GNOME;Application;Development;
   StartupNotify=true
   

   And save the file

6. Launch Eclipse

   /opt/eclipse/eclipse -clean &

7. Now you can Lock Eclipse to the launcher bar by clicking right button on Lock to Laucher

I recommend you to download directly from the eclipse website. the installation process very easy, just extract the files tar.gz, to remove it is also quite easy, simply by deleting the eclipse folder :D

From your desktop, Click on the Ubuntu Software Center 

Once it opens do a search for Eclipse

When the search is done, you will see Eclipse listed. all you have to do is click on install, sit back and relax until the installation is done.

If you still have any questions, do not hesitate to ask.

This is the instructions copied from http://www.inforbiro.com/blog-eng/ubuntu-12-04-eclipse-installation/

How to install Eclipse IDE platform on Ubuntu 12.04 LTS Precise Pangolin

1) Open a terminal and enter the command

sudo apt-get install eclipse-platform

2) After Eclipse is installed you can install development plugins based on your needs, e.g.:

will install Java Development Tools (JDT) package for Eclipse

sudo apt-get install eclipse-jdt

will install C/C++ development tools packages for Eclipse

sudo apt-get install eclipse-cdt

Always download the packaged eclipse from their website. Its best for you to place the eclipse.tar.gz into your opt directory and create symbolic to it and use that around your system.

So if you end up upgrading in the future, all your shortcuts and links wont die.

This is the preferred setup for eclipse. IMO

I created this little script to install on a bunch of Cinnamon machines. You might have to change specific stuff for your needs but you can use this as a template for your own.

#!/usr/bin/env bash

wget -P /tmp/ http://eclipse.mirror.triple-it.nl/technology/epp/downloads/release/kepler/SR1/eclipse-standard-kepler-SR1-linux-gtk-x86_64.tar.gz

tar -xzf /tmp/eclipse-standard-kepler-SR1-linux-gtk-x86_64.tar.gz -C /opt/
chown -R root: /opt/eclipse/

cat <<- ‘EOF‘ > /usr/bin/eclipse42
    #!/bin/sh    
    export ECLIPSE_HOME="/opt/eclipse"
    $ECLIPSE_HOME/eclipse "$@"
EOF

chmod +x /usr/bin/eclipse42

cat <<- EOF > /usr/share/applications/eclipse42.desktop
    [Desktop Entry]
    Encoding=UTF-8
    Name=Eclipse
    Comment=Eclipse IDE
    Exec=eclipse42
    Icon=/opt/eclipse/icon.xpm
    Terminal=false
    Type=Application
    Categories=GNOME;Application;Development;IDE;
    StartupNotify=true
EOF

You can now run Kepler by typing eclipse42 or wait for the menu to refresh (or enter restart) to find it there.

Feel free to comment changes you‘d recommend.

If you are asking about the eclipse classic the latest version from the eclipse project is 3.7.2: and you you can download the tar ball from the website for your OS here:

http://www.eclipse.org/downloads/packages/eclipse-classic-372/indigosr2

The latest version in the Ubuntu Software Center is Eclipse 3.7.1; either download it from there or use the terminal with this command line:

" sudo apt-get install eclipse && sudo apt-get update "

As far as a PPA? There appears to be no current or maintained PPA for eclipse classic. The PPA page at LaunchPad still exists but there has not been any activity for what appears to be two years now. You can check out the PPA page here:

https://launchpad.net/~eclipse-team/+archive/ppa

The best way to install eclipse classic and the latest version 3.7.2 is from the Eclipse Classic project download page for your OS version. Warning: Eclipse 3.7.2 is built and developed for Ubuntu 10.04 LTS according to the Eclipse Project "Read Me" html documentation. There have been known "will not start issues" with later Ubuntu versions due to the compatibility of Java Runtime Enviroments; it works with JRE6 rather than JRE7. Good Luck :)

As with any other Eclipse version, you don‘t have to get it from the repositories. Just download the appropriate archive from eclipse.org, extract and run Eclipse.

Eclipse in the repositories is often outdated. It is usually updated every ubuntu release.

mkdir ~/opt

Change directory to the folder where your browser downloaded the Eclipse package to. Then unpack Eclipse into the opt folder:

cd {directory where your browser downloaded the package to}
tar -zxvf eclipse-jee-juno-SR1-linux-gtk.tar.gz && mv eclipse ~/opt

Make a bin folder in your home directory, this will be used for the startup script:

mkdir ~/bin

Next create an executable for Eclipe at ~/bin/eclipse with your favorite text editor by typing vi ~/bin/eclipse or nano ~/bin/eclipse into the command line. Add the following content:

export MOZILLA_FIVE_HOME="/usr/lib/mozilla/"
export ECLIPSE_HOME="$HOME/opt/eclipse"
$ECLIPSE_HOME/eclipse $*

Finally, allow the script to be executed:

chmod +x ~/bin/eclipse

HINT: If you are a gtk user and experience problems with the mouse buttons you should try add an export:

export GDK_NATIVE_WINDOWS=true

to the starter file.

You can now execute that file to start up Eclipse.

If you have already installed eclipse from the software center, there is an easier way.
If you haven‘t, do that first.

cd ~/Downloads  # (or wherever your tar.gz is)
sudo tar -xf eclipse.*.tar.gz ‘/opt‘
sudo ln -s /opt/eclipse/eclipse /usr/local/bin/eclipse

Note: much of this process is just tweaked from the top answer to be easier.