There are many facets of safety. Usually they boil down to don't's, do's, and bike sense. We need to know the fundamentals and then review some advanced advice, preferrably before we need it. Bicycle safety can be divided up several ways. A page has been dedicated for each topic.

The best way to remain safe while riding a bicycle is to remain alert and know your limits.

Here's a good site for safety that isn't lame:

Bicycle Safety: How to Not Get Hit by Cars