When you say black and white, do you mean true on/off colour, or do you mean greyscale? ^_^ I know
I wouldn't want to even try making backgrounds and sprites with just black and white, 1-bit style.
However, if you mean greyscale (like I assume you do) then I suggest you take a look at old Gameboy games, particularly:
Final Fantasy Adventure
The Legend of Zelda: Link's Awakening
Both of those are quite good-looking games (especially Zelda) which use only four colours: white, light grey, dark grey, and black. I'm sure a look through MobyGames' Gameboy section will get you a look at good and bad examples of greyscale games (screenshots link is in the left-menu once you click into the game).
As for suggestions, I think a basic idea with greyscale graphics is to keep the backgrounds quite simple, and lay the detail on the characters. This way, the eye is naturally drawn first to the characters, and they will tend to stand out from the background. Having played a fair number of gameboy games back when a gameboy emulator used up most of my computer's resources to run, I can tell you that the easiest way to make your game ugly and unplayable is to have backgrounds that confuse you as to what your character is.
I don't know if you'll be aiming for a 2-bit (four colour) greyscale like on the gameboy, but it's always good to be able to work with as few colours as possible, and then consider any extra colours a treat. :) Good luck! I am interested in seeing what you're cooking up over there.