(Updated 2/19/11 for clarity, rewrite of helmet section)
Helmets
Please note: after reviewing my references, I have rewritten my opinion on helmets somewhat. Last update 2/20/11.
Helmets are quite valuable for children, and I think also for off-road use. Children invariably fall down, and off roading involves a certain number of rocks and trees. Helmets have a lot to offer against falling, and against rocks and trees. (I'll cite a study on children:
http://pediatrics.aappublications.org/cgi/content/full/110/5/e60)
But how much do bicycle helmets offer adults against traffic? Here is a recent tragedy in which the cyclist was wearing a helmet:
http://www.deseretnews.com/article/705366912/Teen-who-hit-and-killed-bicyclist-in-Magna-charged.html
Clearly not every accident is survivable, no matter the helmet.
Ken Kifer was formative on my earlier opinion: http://www.kenkifer.com/bikepages/advocacy/mhls.htm. For one thing, he points out that helmet testing specifications are insufficient for protection in traffic. (Ken's thesis is against mandatory helmet laws.)
Scientific studies of adult use in traffic provide two conflicting pieces of information: 1) that helmets do reduce head injuries, 2) that helmets don't significantly reduce mortality in populations.
http://depts.washington.edu/hiprc/practices/topic/bicycles/helmeteffect.html
I think what needs to be understood is that a helmet protects only one vital organ, that it does nothing against the crushing weight of a vehicle, and that even a helmet cannot protect your head sufficiently in many collisions.
In short, a helmet may help but it does not make you safe.
What I want to argue is that discussions of bicycle safety are wrong to focus intensely on helmets. We know that bicycle helmets are deficient for use in traffic. Our focus should be on accident prevention. An ounce of prevention is worth several pounds of the helmet cure.
All that being said, I personally wear a helmet because it doesn't hurt, and anything that improves my chances of reducing injury or escaping death is worth it, so long as the prevention is reasonable and the chances are significant. I think a helmet offers significant protection, if incomplete. (I also need something on my head to tie my flashing P7 LED headlight to, as a measure of prevention.)
Technique
Technique belongs right at the top of a bicycle safety discussion. Your most valuable tool of prevention is your brain. There are many good web sites on this subject, but here is how I ride, and a few pointers:

Those more familiar with cycling technique will note that my above notes outline "vehicular cycling," but this is not the only school of thought. For example, there are a few cyclist who really believe that riding against traffic or on the sidewalk is better. I disagree overall, however I don't think that is so fundamentally unsafe or slow that it can't be done - but anyone who chooses to ride against traffic needs to really understand that they are generally invisible to everyone. If you have the right mindset, maybe that's okay, but not for me.
http://www.kenkifer.com/bikepages/traffic/index.htm
http://www.bikeforums.net/forumdisplay.php/8-Advocacy-amp-Safety
Safety Statistics
Statistically speaking, there are about 800 bicyclist deaths every year in the US. It would be helpful if I could somehow calculate my own risk, using a comparable population riding a comparable number of miles on comparable types of streets. Too bad that is impractical. In fact, I can't even get a hard number on the basis of risk per mile, because we don't know with much accuracy how many miles US bikers ride per year. Instead of trying to work this out myself, I'll refer to Ken Kifer:
http://kenkifer.com/bikepages/health/risks.htm
Ken used the high number 21 billion miles per year, essentially because he couldn't believe the low number 6 billion. According to his calculation, bicycling is around 2.5 times more dangerous per mile (in risk of death) than driving or riding a car, which makes it about the same risk per hour. If by chance Ken is wrong and the low number is correct, then the risk could be another three times greater than that.
(Ironically, Ken Kifer was killed by a drunk driver in 2003. It doesn't make me feel a lot better to know that the driver was convicted of murder for this. I hope that such cases would act as deterrents to drivers who would endanger others, however I've seen a lot of bad driving, and I don't believe it. If I were killed by some jerk, he indeed ought to be prosecuted as a criminal, but it really wouldn't make that much difference to me (being dead), and I doubt that it made much difference to poor Ken.)
Assuming that I ride my bike to work 3 out of 5 days from now until I'm 60, I would ride a total of almost 100,000 miles, divide by 21 billion and multiply by 800 and my statistical lifetime risk of death on my bike commute appears to be about 0.4% or 1:270. On the other hand, if I use 6 billion instead of 21 billion, I get 1.3% or 1:76 lifetime risk of death while commuting. Either number doesn't appear to make a huge increase in my risk of traffic mortality, compared to the average American's lifetime risk of dying in traffic (around 1:60 or 1.7%).
(Part of the reason this is so marginal is that I've put my annual bicycling miles at only about 3,000 per year, whereas the average American drives over 10,000 miles per year, also I'm limiting the age range over which I'd be doing this (more on that below). The risk per mile is higher, but the total number of miles is much much lower than that I will drive.)
The problem with statistics is that they apply to populations, not to individuals. Real world risk is not per mile, but rather risk is per pass, per intersection, and per lapse in judgment, and it depends a great deal on how I ride, which roads I choose, and how vigilant I am. (Of course there is a completely random element as well. That drunk loser is going to kill someone tomorrow night, if I'm in the wrong place at the wrong time I probably can't prevent it from being me.)
I suspect driving habits in the car are an indicator of bicycle safety. I'm not as safe of a driver as I could be, but I think I'm reasonably safe - I've had a few very minor collisions, but I like to say that I've never bent a fender. (As an aside, I'm totally mad at my mistakes and I swear I'm going to do better. It's not as easy as it sounds: traffic habits and personality are intertwined.)
A few sources have pointed out that the health benefits of exercise outweigh the risks of cycling in traffic by 6:1 or up to 20:1. However, there are certainly much safer ways to get exercise, such as a treadmill or a stationary bike. I think most people agree that walking or jogging (on the street) is not safer than bicycling, although I believe that conclusion depends a great deal on the choice of roads, time of day, dress, and it may not be true at all when you look at it per Calorie instead of per mile.
In my own case, I own stationary exercise equipment, and my employer gives out almost free gym memberships, but I still feel that there are benefits to exercising while commuting - because I have to commute on a very regular basis, but I don't have any particular deadline for exercise - it makes it easier for me to make time. I also gain a little time that I would have spent driving. Also, let's face it, stationary aerobic exercises are intolerably dull. Anyone who has actually managed to stick to a routine on a stationary bike or treadmill - good job, I can't do that, you're a wacko.
Lastly, it has to be pointed out that failure to exercise creates a risk that crops up starting around mid-life, generally after age 45 and especially over age 55, whereas cycling now creates a risk right now. If my big worry was dying before age 40, then not exercising is the way to go. (Or exercising on stationary equipment is even better.)
It's also worth pointing out that accident survivability drops with increasing age. If cycling is really for me, it's still worth considering that maybe I should get off the bike and move to a safer exercise when I get to around age 55 or 60.
Get off the bike just when I reach heart attack age? Where are the health benefits then? First of all, I think there's a big difference between reaching 60 in excellent fitness versus reaching 60 in decrepit fitness. It's difficult for unfit people to become fit, and this difficulty becomes steeper and steeper with age, as joints and bones grow weak and uncooperative, muscle recovery grows longer and more painful, and habits become mentally cemented. Second of all, I'm expecting (or trying) to achieve some other lifestyle changes that will fit into this whole scheme. Namely, that I want to be self-employed (and not commuting) before around 45 or 50, and especially I want to be working fewer hours before 55 or 65, such that I might have a lot more recreational time in which I can have more fun exercise, such as hiking and swimming.
http://en.wikipedia.org/wiki/List_of_causes_of_death_by_rate
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The safety of horns, communicating through action, and wigs.
I heard in an NPR radio segment that there are actually very few legal uses for a car horn that actually increase safety. In most states a horn must be used for emergency purposes only. So honking at the guy stopped in front of the green light while staring off into space can get you a ticket. Their main point was that in a real emergency, most instances when a horn is used in a car, steering and breaking would have been more effective actions to take. Replacing a horn with a big metal spike might actually increase safety, because everyone would be much more careful drivers.
Since awareness by other road users is a particular problem for bikes, I imagine there is more benefit from making some noise. Personally, I usually yell or scream, since it keeps my hands free to do other things, like pray. In fact, a close call with an oncoming vehicle turning left taught me that I can scream, brake, swerve and leave a brown spot in my pants all at the same time. I'd say I was chewing gum too, but that would be bragging.
One thing that I have noticed really helps in riding with traffic is making sure your intentions are clear through body language and action. If you're indecisive or timid, drivers don't know what you intend to do. I see this a lot at 4 way stops, when the cyclist has right of way, but hesitates for a second, the driver takes that as an indication the cyclist is yielding. Then they both enter the intersection at the same time, and confusion ensues. I notice this a lot at trail crossings too. The highway 520 trail in Redmond has several trail crossings at freeway off-ramps, and hesitating at all seems to be a green light for the driver to cut you off. So, I usually slow down but keep moving my pedals forward to make it clear I intend to continue through the intersection.
As for helmets - you might be better off wearing a blond wig: http://news.bbc.co.uk/2/hi/uk_news/england/somerset/5334208.stm
Re: Horns and wigs
I agree, but I defy any officer to cite me for my horn use. 1) Sometimes I use it preemptively, i.e. a crossing car is approaching stupid fast and I can tell what he's about to do. (That one is probably legal.) 2) When I'm angry. (Maybe not so legal.) Actually I probably go 50-100 miles between using it. It must be the least valuable thing on my bike. The one time I've had a near miss it was indeed the hollering and swerving that got me out of it alive. (That was before I put on the P7 lights.) The only legitimate use for a horn is to prevent the near miss in the first place.
Sometime soon I need to put up a review of my lights. The flashing P7 light on my helmet is an attention-grabber even in full daylight. (Brighter than most of the low-beams and some of the high-beams on the road.) Now all I need is a wig-mounted P7.