tubechallenge.com

You might be interested in an article in this month's Underground News about someone who did an LUL in a day challenge. He not only visited every station, but every stretch of the Undergound except for the Watford Curve in about 20 1/2 hours.
However he allowed himself to use a bike between stations. From having a look at his log it seems that it could actually be done in the same time without using a bike but with a different route or different connections.
I scanned the log, you can find it here.

How quick can all stations be done with a Brompton then?

There is a discussion about this currently going on in uk.transport.london - see http://tinyurl.com/g3pq8

A real oddity - missing out some parts that are licenced for public use (Rickmandsworth Curve & Kennington Loop) just 'cos he felt it reasonable.

Can I have a go at Tube Challenge, but miss out the Northern Line 'cos it smells a bit funny?

There were two reasons mentioned for not doing the Rickmansworth Curve, one was that it was not on the map. The second was that he wouldn't have made it otherwise. Sounds indeed very odd. The Kennington loop is different in my opinion. There are no scheduled passenger services along this part.

Ricky is not on the map, but it is timetabled, so I think it should be included.

True, the Kennington Loop is not an official service, but it is licenced for carrying members of the public, so it is debateable whether you should include it, but it would be fun.

Rickmansworth is just 1 train though isn't it?

Rickmansworth north curve certainly has more than 1 train a day over it!

These are (Mon-Sat):
0519 Chesham- Watford
0549 Ricky- Watford
0604 Ricky- Watford
0048 Watford- Ricky

The north curve is the only bit of LUL I need to traverse, but due to the train times it is very hard to do (and there is hardly any bus routes running that early in that part of Herts!)