i too am fearful of traffic - especially since i live in manhattan - specifically, times square. traffic here is nuts. i live on the west side and ride my bike on some quieter streets/sidewalks while i head over to the bike trails. once im there, it's 13 miles of uninterrupted bike path - no cars at all.
i dont know if i'll ever get over it. and while true, the suggestions above are great, i still will not ride in traffic like so many people do. i saw a commuter get his rear tire run over by a minivan - thank god he was okay.
and not to mention the several "ghost bikes" that i see around the city that represent people that have died on their bike.... i dont want to become a statistic.