For 11.10 and above
The older GNOME 2.x experience has been retired in GNOME, however you can use the GNOME 3.x classic mode to make an approximation of the older experience.
install prerequisites
In the software center you have the option to install Gnome Shell

Similarly - search for CompizConfig Settings Manager and install this package - we'll need that later.
Whilst you are there you can also install "Gnome Tweak Tool" to further customise your desktop.
enabling compiz
Now perhaps the tricky part - getting gnome classic to function with compiz:
In a terminal copy and paste the following:
gksudo gedit /usr/share/gnome-session/sessions/gnome-classic.session
Now edit the file shown to contain this line entry:

How to login to Gnome-Classic
Save, logout and in your session options choose Gnome Classic

Changing the theme
You'll notice that the default Ubuntu Ambiance theme doesn't look great in Gnome Classic. We can correct this by changing to a Gnome 3 friendly theme.
for 11.10 (oneiric)

for 12.04 (Precise)

for both
... and choosing Appearance 
Change the theme to Adwaita...

Note - see the linked questions below for other theming options.
Changing Icons
Launch gnome-tweak-tool via the menu option:
- For 12.04 (Precise): Applications --> System Tools --> Preferences --> Advanced Settings
- For 11.10 (Oneiric): Applications --> Other --> Advanced Settings
Change the icon theme as shown:

Restructure the desktop layout
Now lets get back the panels to something that we are familiar with...
Press Win+Alt and right-click the top menu bar - N.B. Win is the Windows Symbol key

(If you are using Gnome Classic (No Effects) i.e. gnome fallback mode then to add to the panel use Alt and right-click)
Choose Add to Panel

Click the option shown and click the button Forward

Repeat the Win+Alt + Right Click the date and choose Delete to delete the clock.
Repeat this delete procedure for the other applets on the top-panel.
Note - if an error appears indicating that the Panel has reloaded you can safely ignore this.
Repeat the Win+Alt + Right Click the top panel - add the applet Accessibility.
Repeat the Win+Alt + Right Click on bottom panel - add the applet Show Desktop and move to the bottom left.
Repeat the Win+Alt + Right Click on bottom panel - add the applet Wastebasket and move to the bottom right.
Now we need to change the number of workspaces back to two.
Navigate to Applications - Other - CompizConfig Settings Manager - General Options - Desktop Size and change the Vertical Virtual Size value to 1

Install the indicator-applet
Now lets install the indicator-applet:
- For 11.10 - see this linked question to add a PPA containing the indicator-applet
- For 12.04 (Precise), you need to install the package
indicator-applet-complete
To add to the panel:
Win+Alt+Right click the panel and choose Add To Panel and add the following indicator

Finish off by Win+Alt+Right click the indicator-applet and move it to the right side of the top panel.
Final Result...

Optional:
- You can install fonts-cantarell if you want to use the default upstream GNOME font
Linked Questions:
- Delete extra toolbar on top of the screen in GNOME fallback mode?
- How do I revert Alt-tab behavior changed in 11.10?
- How do I change the theme?
- If you use autologin you need to do this: How do I set the GNOME Classic login to be the default with autologin?
- GNOME 3.2 in 11.10 blog post from one of the maintainers
- How to re-add indicator-applet for 11.10
- How to customize the gnome classic panel
- Warning: What are some of the issues with ccsm and why should I not use it?