The London Evening Standard has figures on crime by tube station, care of the Transport Police, here. Tube stations which share an entrance with overground stations appear to have been excluded, so there is no data for, inter alia, Richmond, Wimbledon, Kensington Olympia and Upminster.
The most crime ridden stations appear to be the tube interchanges with the mainline stations. Well knock me down with an integumentary appendage....
Because I am a bit of stats nerd, I have been contextualising those crime figures to annual entries and exits at stations (2010) on the District Line (Well, I'm not going to do the whole network, the D-Line is the one I use most and it goes through a number of mainline stations). And that makes things look rather different, with West Ham emerging as the most crime ridden station relative to use, with 43 crimes reported for its 3.39 m entries and exits, or a figure of 12.7 per million. Note that this is not the home station for West Ham United, that being - as any fule kno - Upton Park. Upton Park has a figure of 3.4. At the other end of the scale is Barking at 2/13.72m, giving a figure of 0.145. This makes West Ham some 87 times more dangerous.
The top six most dangerous stations are all in East London - West Ham, Dagenham East (11.4 per million), Becontree (8.4), Upney (5.3), Plaistow (4.7) and Upminster Bridge (4.49). The seventh is Notting Hill Gate (4.4).
There are two very serious mainline interchanges on the D-Line - Victoria and Paddington. Those two have figures of 2.3 and 0.86 respectively. This makes Victoria safer than Ravenscourt Park (2.38) but more dangerous than Mile End (2.19). Paddington is only marginally less safe than Turnham Green (0.84), here in leafy and riot-free Chiswick.
Despite the tendency of some of the locals to loot and pillage, Ealing Broadway was a pretty safe place to enter or exit in 2010, with a figure of 0.48 per million, a figure bettered only by Barking and Aldgate East (0.22). Cannon Street also fares creditably at 0.51, making it safer than Gunnersbury (0.76) and Stamford Brook (0.80). The nation's Parliamentarians are safer at Westminster (1.5) than users of Barons Court (1.7) and Embankment (1.8), if in greater peril than travellers making use of South Ken (1.57) and Chiswick Park (1.55).
I had intended to map this information, but a full tube map would be too crowded, and a diagrammatic map of the D-Line has proven google resistant. However, I have a plan which may yet see the light of day.
I will answer requests for figures for individual stations, should this have piqued anyone's interest.