Please post your safety tips for cycling/commuting that should help you get to your destination place in one piece.
I came across a nice printed guideline a few years ago when working as courier, it was posted on the wall in the base and covered many common road situations. Recently I tried to look it up on the web but with no luck, so I thought that placing a community wiki question here could be beneficial for many commuters.
A lot of cyclists promote vehicular cycling in which you act just like a car, obeying all of the rules of the road. This includes respecting all stop signs & lights, travelling in the same direction on the same side of the road as motorized traffic, and using the full lane (taking the lane), often ignoring marked bike lanes if they are too small or marginalized.
To me, vehicular cycling means acting like you belong on the road and that you have the legal right to be there (which you do). I think a lot of bicycle accidents happen because the cyclist is trying to stay out of the way of cars and in doing so becomes very difficult for cars to see.
This answer is community wiki - please feel free to modify
To give it a good start here are some main points that I normally follow:
never take turns on the inside beside a turning car, and definitely not along a bus or truck - I believe that is the main cause of fatal accidents involving cyclists - long vehicles cut the corners when turning and you may end up without any space left and no way to escape
when passing parked cars or vehicles stopped in traffic try to maintain safe distance in case a car door is opened, if maintaining safe distance is impossible make sure that no door is going to be open in front of you; watch for people moving inside the cars, or simply slow down or stop
when stopping at traffic light, move to the front of the traffic so the drivers can clearly see you (some cyclist friendly junctions have dedicated space for bikes at front of the traffic)
when approaching junctions move slightly to the middle of your traffic lane so if a car wants to overtake you it needs to change the lane, that way you will ensure that no car will suddenly pass you and tun in front of you.
when approaching junctions do not pass the vehicles on the inside - not all the drivers indicate turns, many do not see you, cars have blind spots
be extra careful when cycling in the rain, many drivers do not see you in normal conditions - with rain it becomes even worse, I believe that using High Visibility stuff in rain is a must (if you are also a driver I think you agree)
There also a book called The Art of Urban Cycling, in which the author focusses on bicycling safety amidst traffic in many different situations. I have not read it, so I'm not sure if it's any good, but it could be worth checking out.
My top tip - as you approach junction, if there are drivers waiting to turn into or across your lane, watch their eyes. You should be able to tell if they see you, or if they are scanning only for large objects (i.e. other cars).
Here's a related awareness video which shows why its easy for people to not see cyclists if they are concentrating on other objects.
Some tidbits that have kept me safe over the years:
Learn to glance over your shoulder (BOTH of them) without veering off a straight line. I've seen a lot of people glance over their shoulder for one reason or another and get into trouble.
Be able to hold your line while pedaling. What I mean is when your are pedaling (especially up a hill or something like that), don't slightly swerve back and forth. This tends to scare drivers, and you don't want scared drivers passing you.
Use active lights at night (front and rear). Those passive reflector only work at a few angles. Reflective jackets work, too, but blinkies can be seen from a long way off.
Don't be afraid to take the lane, but make sure you glance over your should before you do.
Concentrate on what is in front of you rather than what is behind. Every time I've seen a car on bike accident it has been because the biker was not looking ahead. People driving are usually paying more attention to the road (one would hope). Most of the accidents I have seen are doorings (google it) and cars pullout out of spots. The tricks for those are watching the mirrors of the cars for faces and the wheels for any movement.
Check your bike completely before you ride. This involves the brakes (they should both be able to take your full body weight by leaning against them, so to speak), the tires (low air pressure makes handling strange and sometimes unpredictable), and the drivetrain (is it clean and properly lubed).
Get used to getting out of the saddles to maneuver.
Learn to stop your bike as quickly as possible from faster and faster speeds. This involves getting out of the saddle. Make sure to adjust your stopping distance (i.e. how far you look ahead) to a much larger distance when conditions are wet (if you ride in those conditions).
Always wear your helment.....every time.....no exceptions! This is because the human brain has the same consistency as tofu.
When considering whether or not to do something illegal (run a stop sign, for instance), ask yourself is the few minutes you'll save potentially worth your life. This is one rule I don't follow very well because I'm overconfident a lot of the time, but I'm trying to change that.
Over time you'll probably develop more intuition than can reasonably be explained here, mostly because it has very much to do with where you are riding.
As well as these great answers I think it's also important to set a good example when driving. Before I cycled on the roads (I used to be purely offroad rider) I never gave much thought to cyclists, just squeezed past like everyone else. Now I do the following:
Slow down as soon as I get near a cyclist
Put my indicators on, ready to overtake
Wait for a suitable place to overtake
Use the whole of the other lane for my overtaking manuevoure
Move back in, ensuring I've left the cyclist plenty of room
It sounds like obvious stuff, but I've been watching the drivers behind me in my rear-view mirror and a lot of them will copy the same overtaking manuevoure as you. The more drivers we can get to overtake safely, the safer we'll all be.
Eye Contact is a very good way of making sure drivers have seen you - particularly for cars waiting to pull out of side junctions or at roundabouts. When coupled with a friendly nod once you're passing them (almost as if to thank them for waiting) you'll find that many of them will then give you a proper amount of space if they need to pass you afterwards.
Familiarize yourself with bicycle laws where you live and ride. In the US many (most? all?) states require cyclists to adhere to the same set of rules that apply to motor vehicles when riding a bicycle on public roads. Some additional rights and responsibilities may also exist depending on where you live (for instance, where I live cyclists are allowed to pass on the right).
Most importantly, once you know what the rules of the road are, follow them! The other day I was in the city and a woman on a bicycle passed me driving the wrong way on a one-way street. If you get into an accident doing something like that, most likely you will be liable!
You need a loud horn if you want to be able to travel fast. That makes your cycle more enjoyable, because people won't get in your way, and you can warn cars that aren't driving well. E.g. the Hornit electronic bike horn. Alternatively, a bell can help - it's just not as loud. I use both a bell and a horn, for the different volumes.
Cycle 1m away from the kerb if you don't have a flag that extends sideways. That way, cars don't take advantage of you as much as if you hug the edge of the road, and they often, but not always, overtake with more room. This relates to the "vehicular cycling" mentioned in the top answer. The first prize is to get a flag that you can flip vertically and horizontally, because then you can cycle close to the edge and cars will always be forced to give enough room when overtaking. For an example, see www.flipflag.co.za .
Your visibility is KEY. To be more visible use flashing front and rear lights even during the day; stand up on your pedals at intersections so that you appear larger; whenever possible ride in a group as the visibility of a large group is greater than even a car.