Here are some things I do to remain safe on the roads:
1. Always wear your helmet, even when just testing your bike in the driveway, riding between your car and the registration booth at a race/event, etc. Always put the helmet on.
2. Use lights always: We have daytime running lights on cars so do the same on your bike. Front and rear lights always on can only help make you more noticeable.
3. Wear bright clothes: The typical black bibs/shorts may be unavoidable but use brightly colored jerseys and jackets.
4. Use a mirror: Its amazing to me how few riders use a helmet mounted, eye-glass mounted or bar-end mounted mirror. You wouldn't drive your car without one so why ride without one? I use mine in time trials unless the road is closed (the eye glass mounted type). In casual riding, training and racing, I glance back when I hear cars approaching. I use it to change lanes although I still turn and look. It's indispensable when turning left and you have to stop in a non-turn lane. Its also a great way to know if riders are dropping off the pace. Mirrors aren't regarded as 'cool' since the racing crowd would never wear a mirror when training but I think they are essential to safe riding on roads.
5. Take the lane: If there are two lanes in your direction and not enough space along the white line/curb to ride and allow cars to pass, take the lane, and make it obvious. On single lane roads I try to stay close to the white line to allow traffic to pass but if it looks like I may get squeezed when opposing traffic would cause a passing car to push me off the road, I'll take the lane until things are clear.
6. If possible ride outside the white line: No need to take the lane when the shoulder is wide enough for a bike. Cars will love you for it.
7. Never run red lights or stop signs: It's dangerous and will just make the other users of the road mad. It gives us all a bad reputation. Act like a car and drivers will treat you like one.
8. Left hand turns are very dangerous: A mirror helps since you're standing or balancing while traffic approaches behind you. Be emphatic with your hand signals. I've bailed on left hand turns if traffic is too heavy. If needed, a few right hand turns will work just as well.
9. Never go through an intersection without looking both ways just to be sure no side traffic is coming. It's little consolation knowing you had the right of way when a car hits you.
10. Pick times of the day to ride with lighter traffic like early mornings before rush hour, mid mornings, or after evening rush hour.
11. Pick your roads: While bikes are allowed on most roads that doesn't mean these roads are safe. I'd rather add some miles (thats always good) by taking out of the way and lightly traveled roads.
12. Keep your head up: Running into a vehicle or stationary object because you were head down is completely avoidable. Look ahead, always.
13. Do your interval training on the safest roads possible: Concentrating on power, HR, cadence, etc is distracting. Trying to deal with heavy traffic at the same time add's substantial risks. Pick your roads carefully.
14. Never get into it with a motorist unless you are immediately physically threatened. A driver who passes by and honks or yells trying to frighten us is just an idiot. Let it go. Someone trying to run us off the road is a direct threat but they'll likely keep going. If you get the license plate, turn it in to the police. They may or may not do anything (likely not). Someone stopping and making threats should be avoided. Try to defuse the situation. You never know what they have in mind or have on them. Then again, should they become physical, you just go for it defending yourself. Most of the general population is pretty out of shape. Go for the larynx. The Survive Institute says its the best way to stop someone. It may be worth the 'are you willing to take the chance that I may be an off duty cop' comment to scare them off. You didn't say you were, just that you might be. I've actually used this locally and in Great Smoky Mountain Park. In the latter, some college idiots drove by me and tried to scare me by hanging out the window and swerving their vehicle. I happen to see them not far up the road at an overlook. I mentioned that I might be an off duty ranger. They all of a sudden became very apologetic.
15. Use hand signals: Let drivers know your intentions. Cyclists, when driving a vehicle, may have a better sense of what a fellow cyclist is going to do o the road but to most drivers we're just another road obstacle they have to worry about. Be obvious with your turn signals, when stopping, etc.
16. Make eye contact: This is an add-on to #15. make sure people see you and acknowledge you.