Where has the cartogram plugin for QGIS gone?

The latest version of the Cartogram plugin, which works in QGIS 2.2, is here: https://github.com/CristianCantoro/cartogram-plugin , pending a pull request.

To prove it works in 2.2 I created a bendy map of London with it:

carto http://dl.dropboxusercontent.com/u/15008199/Images-2-share/carto-2.2.png

To install, unzip/clone the repository into the qgis2/python/plugins folder. E.g., this is how I did it on my Linux system:

mv repos/cartogram-plugin-master ~/.qgis2/python/plugins/

You should then find the icon in QGIS's top bar next time you load it.

Carson Farmer's repository may be out of commission for the time being, however there are a number of other options for creating cartograms like the one you described.

Cart, by Gastner and Newman using their diffusion-based method http://www-personal.umich.edu/~mejn/cart/

Cartograms, by Widdle (for Windows) http://www.griddle-gidata-analysis.com/page2.htm

ScapeToad, by Choros Laboratory using the diffusion-based method: http://scapetoad.choros.ch/index.php

Provotis, by Stanford Visualization Group includes tool for Dorling Cartograms http://mbostock.github.io/protovis/

IndieMapper, by Axis Maps produces noncontiguous cartograms http://indiemapper.com/app/

In 2.12 it (Cartogram plugin version: 1.0.0, on windows 10) works fine, just did a check.You have to wait a few seconds...