Most sources put it around 2.5x more dangerous than driving, and I'd wager most of those deaths come from inexperienced riders who don't know the traffic laws as applied to bicyclists.
Fatalities Per Mile
Motor Vehicle Travel.................... Bicycle Travel
42,000 killed........................... 813 killed
2.56 trillion miles..................... 21 billion miles
0.016 fatalities per million miles...... 0.039 fatalities per million miles
Data from Traffic Safety Facts 1997 and The Environmental Benefits of Cycling and Walking
Pulled from http://www.bellboycott.com/cached/www.kenkifer.com/bikepages...