Using London 2012
All brands, companies and official events are protected by copyright and intellectual property laws this includes things such as trademarks, logos and designs. The Olympics and the Paralympics are official events that are protected by these laws.
Using the Olympics the Paralympics or any representation of these in a campaign or in your SEO without written consent from the London Organising Committee of the Olympic and Paralympic Games (LOCOG) goes against intellectual property rights. Using them without permission can end up with your company becoming fined or getting other penalties. You are only allowed to use events and any representation of them if you are an official broadcaster on sponsors.
As well as LOCOG being responsible for organising and staging the Olympic Games and Paralympics it is also responsible for protecting the integrity and value of the games. LOCOG realised this document with details and information about the marketing rights to do with the Olympics and Paralympics: http://www.london2012.com/documents/brand-guidelines/statutory-marketing-rights.pdf
There are ways around using events which a lot of companies have taken to doing, such as using games on their adverts and using things that could symbolise the Olympics or Paralympics. We found this article giving creative ways to get around the intellectual property laws by The Drum: http://www.thedrum.co.uk/news/2012/07/25/drums-unofficial-guide-unofficially-sponsoring-oymlpics-gamse-2102
Even with the clever ways to get around using the Olympics and Paralympics you should still be careful and make sure you check what you are using against the marketing rights first, as LOCOG will be monitoring the web and media so that they can find those who infringe on their intellectual property rights.