JDWP,
Life insurance is intended to pay out a death benefit in the event that you die while the coverage is in force. Except for the possibility of a VERY limited set of exceptions, it will essentially pay out a death benefit regardless of the circumstances or cause of death.
On the other hand, Accidental Death & Dismemberment (often called "AD&D" coverage) only pays out, as the name indicates, in the event of an accidental death or dismemberment. The latter means that in addition to paying out a "death" benefit in the event that you are killed in an accident, the policy will also pay out its "death" benefit (or a portion of it) if you are dismembered in an accident - for instance, half the death benefit if you lose an arm or a leg, or the full death benefit if you lose both arms or both legs. (Sorry for the gory details, but that's how they're written!)
All that being said, from a financial planning perspective you should be carrying primarily LIFE insurance, and NOT an AD&D policy. Although we all fear the risk and terrible circumstances of an AD&D situation, the reality is that whether you pass away due to an accident or a medical condition, the financial consequences are generally the same (in both cases, you can no longer provide for your family) and thus both need insurance - which means life insurance that pays regardless of the circumstances surrounding the death.
Whatever protection you need to protect your family or other dependents from the risk that you die should be covered using life insurance. Likewise, whatever protection you need to protect your family or other dependents from the risk that something happens and you are no longer able to work should be covered by disability insurance.
Consequently, I don't think there's really a place for any significant AD&D coverage for most people. The circumstances in which it pays are too limited, or put another way - you wouldn't want to leave your family and dependents unprotected because it "happens" that you didn't die or become disabled due to a covered "accident"!
If you want to have a little AD&D coverage because it helps you to sleep better at night, go for it. But it is not a substitute for quality life insurance and disability insurance.
I hope that helps a little!