When you run on the street, one thing you have to make sure you take notice of is the traffic. Cars are coming at you from both directions, and sometimes from the left and right too. It's up to you to be aware of your surroundings and figure out what each car you can see is doing or is going to do. Your awareness on the road while running is really important to your safety. Even a brief distraction can mean the difference between life and death. I'm amazed though at how many runners don't seem to have a clue.
Once while running, I saw a runner in front of me get hit by a car. Luckily, she wasn't hurt beyond a few scrapes where her knees hit the road when she fell, but it could have been a lot more serious. When I talked to her afterwards she said she'd thought the car had seen her and so had continued to run across the intersection. He hadn't until it was almost too late, as he was having an argument with his girlfriend on his cell phone and that was more important than watching the road. If the runner had not assumed he had seen her, she would have waited until he passed and not experienced the scare she did.
The first rule when running on the road is to make sure you run facing traffic. I've seen runners running with traffic coming up behind them. That's so incredibly dangerous, as you have no idea what's coming, how close to you they are or, if they've even seen you. Even if it means slowing down your pace, when you turn onto a new street, make sure you're always running towards traffic.
The second rule is be aware of every car coming towards you. Don't forget, many cars are driven by inexperienced drivers, drunk drivers, drivers who are in ill health or elderly drivers. Any one of these drivers could suddenly do something or have something happen to them (a sudden heart attack!) that could cause their car to head towards you. You want to be aware of where they're heading, and not be surprised when one suddenly hits you head on. Smack! Ow! Dead!
The third rule is always make sure you watch for cyclists. Some people cycle without much of a clue about what's happening around them and, because their brain is looking for something the size of a car and not a person, they can cycle right into you without even knowing you're there. Cyclists also often cycle on the wrong side of the street or go the wrong way down one way streets. This is one reason why it's so important to either not run while listening to music, or keep the music at a low volume so you can hear the bike coming.
Good road safety while running is honestly just common sense. Be aware of what's going on around you. Watch every car you can see and try to anticipate what they'll be doing next. Look out for bikes and don't cross the street until you're absolutely sure that car heading towards you isn't going to hit you. A smart runner is a safe runner and good road sense will ensure you have many happy running years ahead of you.