It depends, its so big! Areas such as Hampstead (NW3), St. Johns Wood (NW8), Hendon (NW4), Golders Green (NW11) Mill Hill (NW7), West Hampstead (NW6) are fine.
Areas within NW1 (Camden Town) and NW5 (Kentish Town) are not to bad, these are where most of the bars/clubs are and you get a mix of people from Goths to Somalians!
The worst NW area by far is NW10, this is the Willesden Junction/Harlesdon/North Kensington area and it really isn't very nice, I am sure its had the highest murder rate in the UK more than Hackney which is a few boroughs to the East. Its a real gangster area with loads of crime oh and its a poor, run down area.
Parts of North London are fine too. Islington (N1), East Finchley & Finchley (N2 & N3), Highbury (N5), Highgate (N6), Crouch End (N8), Muswell Hill (N10), North Finchley (N12/N11), Southgate (N14/N11), Totteridge (N20) and Winchmore Hill (N21) are all fine, actually they are very nice. These areas are full of Middle Class people soeverything is expensive! but they are nice places, you don't have to worry about getting stabbed!
However, there are some horrible places, particulary the eastern part of North London e.g. Tottenham South (N15), Tottenham Hale (N17), Wood Green (N22), Lower & Upper Edmonton (N18 & N9), Stoke Newington (N16). Horrible areas, gangs with knifes, drugs, poverty.
The ok areas are generally N7 (Holloway/Barnsbury) although I wouldn't venture there, N19 (Upper Holloway/Tufnel Park), N4 (Finsbury Park). These areas are not too bad but I would not reccommend going to these areas as they can be dangerous at times.
I would avoid all of East London! the docklands are ok (E14) and the suburbs i.e. Wanstead/Snaresbrook (E11) and Chingford (E4) but areas in E5, E6, E8, E9, E10, E2, E3 are not nice.
then we come to south east london. I don't really venture to the other side but I know that SE1 (waterloo/london bridge) are ok in the day but its a different story at night! SE17 (Walworth) is home to a rough estate named the Alesbury and I have heard its very bad, SE5 (Camberwell) I have been through there at night and there are loads of gangs on the corners! SE15 (Peckham) like SE5, yeah thats all I know about SE London, I know that the suburbs are fine but stay away from hre!
Central London EC1, EC2, EC3, EC4, WC1, WC2, W1 & SW1, these are all fine.
Most of South West London is nice, SW1, SW3 (Chelsea), SW6 (Fulham), SW4 (Clapham; west and south), SW5 & SW7 (Nr South Ken), Wimbledon (SW19) Barnes, Mortlake, Kingston, Sutton are all nice.
Obviously Brixton, Stockwell etc are not nice very rough (SW2, SW9).
West London is very strange, at one end of the spectrum you have the wealthiest area of London, and at the other its the poorest. Most of west London is fine (W1, W2 (Majority not Edgware Road), W4, W5, W6, W14, W10, W11 (parts) are all ok.
Sorry for that very long post, sorry for the bad spelling, sorry for the bad punctuation. I cant beleive that I just wrote all that!
Hope that helped a little!