mea culpa - my base of referral above should be reversed...(in music in MUST think in multiple directions)

Neil is right on target for a mnemonic for remembering # and b's....another is ..."in the key signiture.... take the last added sharp # and go one step higher (for the key it is written in) or take the second to last flat (b) and that IS the key."

In Western Music Culture the cycle of fifths is the most natural progression of tone from one to another. ie. from the note of C....the most natural next tone is F.....(a perfect fifth BELOW or a fourth above.) It is the note that the chord wants to be drawn towards.....the progression is always "moving towards" a tone one fifth below (there may be a by-ways along the path...but they add interest and a sense of anticipation as the listener waits for full fuitiion of the tone. ie: C,F,Bb,Eb,Ab,Db,Gb,B,E,A,D,G,and back to C

I would guess that 70% of all "modern" songs use this cycle.