My Challenges
I've now made sixteen full journeys around the entire London Underground tube system.
The first time I did this was in May of 2002, but it took me until my seventh attempt two years later in May 2004 to set a new record time of 18 hours, 35 minutes and 43 seconds. My ninth attempt was part of the Tube Relief 'We are not afraid' charity attempt.
After moving to America in 2006 for four years, I was away from London and tube, but when I returned, made three attempts [ten, eleven and twelve] in 2010, with varying degrees of success.
In 2011 we were back out again with attempts thirteen and fourteen. Tube 14 in fact got us the second fast time ever in the current configuration. We'll be back out again soon with Tube 15 ...
Write ups of attempts: Tube 1 : Tube 2 : Tube 3 : Tube 4 : Tube 5 : Tube 6 : Tube 7 (World Record)
Tube 8 : Tube 9 (Tube Relief) : Tube 10 : Tube 11 : Tube 12 : Tube 13 : Tube 14 : Tube 15 : Tube 16
In the Media
My third and fourth attempts were both featured on TV. My third attempt was featured as part of the ITV programme 'The Tube' - a general documentary about the London Underground. We appeared in an episode called '24 hours', which was later sold to Sky Travel and often gets repeated on TV this to day.
My next attempt was the also on TV - this time, an entire half an hour documentary featured solely on us and our attempt to get round in the fastest time. The programme was part of the series of 'Metroland' documentaries for ITV, and was called 'Race Around the Underground'. To my knowledge this has never been repeated on TV, which is a shame because I think it's the better programme out of the two.
However, I have a media page here where you can watch both of the programmes.
Tube Relief
In the wake of the terrorist attacks on the tube in London on July 7th 2005, I organised a mass-participation tube challenge event with over 60 people taking part from all over the world. It was not a proper record attempt, but an act of solidarity and defiance to say and show that we were not afraid. We called it Tube Relief (It has its own website at www.tuberelief.co.uk) and we raised several thousands of pounds towards the official charity for the victims and families of those affected in the tragedy.
Other Challengers
I held the record for two years until 2006 when another team beat it by just a few seconds. Since then, several groups of people have got the record time as the tube network has changed (every time a new station appears, or a station if removed from the map the record is 'reset' and is up for grabs all over again). A full list of all the other world-record holding challengers and how the number of stations has changed over the years can be found here.
Zone 1 Only
From the main challenge of doing all the stations on the network, a lot of smaller less-intensive alternative challenges have sprung up and are competed my people on a regular basis. They often involve doing a smaller number of stations so that the challenge can be completed in just a few hours - not all day.
BBC news made a short film of us doing the Zone 1 challenge in 2004, and I made a short-video myself when I attempted it in 2008, both on the Zone 1 page here.
The 
Tube Challenge
The challenge is to travel round all the stations on the London Underground (currently 270 of them) in the fastest time possible. This is a recognised and established world record, that has proper rules and regulations laid down by Guinness World Records. People have been competing for this since 1959.
Geoff 
and Neil set a new world record in May 2004, on their seventh attempt : 18 hours, 35 minutes and 43 seconds.
Have 
a look at the media page for all mentions of the Tube Challenge in the media.
We 
even got written up in the London Evening Standard, where reviewer Victor Lewis Smith upset my mum by calling me 'Super Nerd'.
Links:
History of the Challenge and other challengers
Zone 1 Alternative challenge
The official rules
List of error codes on barrier gates
Secrets of the Underground
Facts & Figures of the Underground
Have you seen this?
Tube Challenge Leagues