For some journeys it's really not worth getting on the tube: it takes a long time, and costs you money. Sometimes it's quicker and easier to walk.
For instance: Leicester Square is only 250m from Covent Garden; Charing Cross to Embankment is about 300m; Chancery Lane to Farringdon by tube requires two changes and 4 stations. Mansion House to Bank: change once, 6 stops - as noted by Bill Bryson in Notes From a Small Island (though you could walk to Bank districtline, aka Monument, and go in two stops, but his point is still well made). Possibly, even Finchley Road to Hampstead (change twice, 9 stops) could be walked in half an hour, although what neither the standard tube map nor the A-Z map will tell you is that it's up a steep hill.
One of the very few weaknesses of the standard tube map is that its distortion of geography (a very successful attempt to present the different stations and lines more clearly) sometimes means that it's not clear when the tube trip is unnecessary. This has been discussed on Edward Tufte's site and in many other places, and there are geographically corrected versions of the map.
But here's a slightly altered map showing which stations are an arbitrary and as-the-crow-flies 500 metres apart from each other (there are many more stations 600, 700+ metres from each other). It doesn't look great yet, and definitely reduces the readability of the standard tube map at the moment, which isn't a good thing. So it's not an improvement on the map, but it's an interesting exercise.
- tube map with 500m walklines dotted in (warning: it's a large 429k gif file, pdf to follow possibly. Nb: our photo album constrains the size of the picture, so click the big versions of these pictures if you want to see them full size); big version here. The dense knots are Euston-Warren Street-Gt Portland St in Bloomsbury and Bank-Cannon St-Mansion House-St Paul's in the city. And these are interesting places to walk anyway.
- And here's the same with the tube map faded out slightly, so you see the walklines more easily. (232k gif); big version here.
- And indeed it might be interesting, for arty folk, to see the walklines without the original tube map behind it. They look like un-named constellations (20k gif); big version here.
- The original tube map used is here (385k gif), and is obviously copyright Transport For London.
Update: Added the bigger versions. Found some more accurate station-to-station distances at Diamond Geezer, who reminds us that you can get this info from the TfL route planner. Also: MUDLondon, muxway, geo-wanking and Antimega are all good for geo/mapping stuff. And Owen Massey has the mother-lode of tube map variants, versions and varia. London Open Guides's Adjacent Stations is a list of stations where you can walk in 15min or less.