Population cartogram from Great Britain
Cartograms are somewhat a double-edged sword in cartography. On the other hand they can make your map look totally distorted and just end up just being confusing. On the other hand they are relatively good in comparing areas very different in size.
Rather than just making one really strange looking map, I think this kind of animation works well in telling the story. What's the story? Population in Great Britain by counties and unitary authorities.
Data
Source: Office for National Statistics licensed under the Open Government Licence. UK Office for National Statistics Geoportal.
Tools
QGIS with Cartogram plugin
Tutorial
Check this excellent tutorial by Tom Armitage. You can also find other useful QGIS stuff from his blog.