There are health benefits due to regular physical activity (and attractiveness and energy level benefits), but they probably don't come anywhere near matching increased risk of death due to drivers completely disregarding cyclists' safety.

An article in an Italian magazine I've read claims a study found the reverse. Among the 181 thousand subscribers of Barcelona's bike sharing service (11% of the population), who cycled in average 3.29 km a day during weekdays and 4.15 km a day during weekends, there appear to be 0.03 more deaths per year (than among the same number of car drivers) from traffic accidents and 0.13 more deaths per year from air pollution but 12.46 fewer deaths per year from sedentary lifestyle. (Plus, cycling instead of driving itself reduces pollution, which affects everybody's death rate, so even if your point is to decrease your own chance of dying there still can be superrational reasons to do that.)