I've been cycling for about 17 years now (since I was 9 or 10 recreationally, started commuting occasionally about 4 years ago, first tour 3 years ago.)
I've never been in a car accident, but I've had a few mishaps due to terrain/bike management that usually amounted to a skinned knee or a jumbled up kit.
Here are a few of the tips that I've gathered to cut the risk of accidents, with cars, other cyclists, or even just myself
1. Try to avoid car-intensive pathways.
As much as possible, I try to cycle either on back roads with fewer motorized vehicles, recreational trails or bike paths with no motorized vehicles, or during off peak times like early in the morning when the numbers of cars is drastically reduced. While this can add an extra hundred yards or two to my trip length, minimizing the number of cars and other shared road users I encounter helps to cut the chances that I will collide with one of them.
2. Research your route
I've gone on short trips and long trips, sometimes lasting several days. Beforehand I make sure to develop a plan for where I'm going to go and the types of terrain I'll encounter, so that I am not surprised when I'm required to go over a train bridge or the road turns to gravel. If I ever have to proceed into "uncharted territory" due to short term construction in an area I haven't been before, I make sure to proceed with caution, and sometimes I've even gone back to avoid the potential hazards.
3. Stay Visible
High visibility clothing is a major factor in keeping yourself safe, and best coupled with a high visibility bike. I like to have lights and reflectors in as many places as I can: Front and back lights, red blinker in the rear, lights on my helmet, reflectors on the seat tube/bag, pedals, for a while I even had a big reflector on my backpack. Every little bit counts when you are riding in the twilight or at night, when drivers and other road users might be battling distractions or exhaustion.
4. Keep your eyes moving
Often times, especially on a long haul ride, you end up picking a spot about 15 yards in front of your bike and start riding into it. The exact length from your bike varies on the person, but this is a terrible trap, because when you stop scanning around for potential hazards and start shutting out the world, you set yourself up for a tumble or worse. Tunnel vision is as dangerous on a bike as it is for a car driver. You need to scan frequently to take in other road users, their speed, and potential hazards on the road itself.
5. Know your limits
The more exhausted you are, the less aware you are. I remember the last time that I met the gravel, I was at the tail end of 120 miles and dog tired, and I just didn't notice the dip in the trail I was riding for the first time. The last time I tasted concrete, I was trying to ride faster than my skills could take me, and I brushed the sidewalk with my front tire, sending me sideways and, had I been in a heavily trafficked area, into the path of a car. Luckily it was around 6AM in the middle of nowhere, so I picked myself up, dusted myself off, and kept riding. It's OK to work yourself at your limit, but not beyond it, or else you aren't being safe.
And of course, wear your helmet in case you end up eating pavement anyway.
Any more tips for avoiding accidents? I'd love to hear them!