According to the Centers for Disease Control, "Even after being visibly rinsed clean, toothbrushes can remain contaminated with potentially pathogenic organisms." Yuck! Here is how to get your toothbrush clean.

[edit] Steps

Keep your toothbrush in a cabinet or use a toothbrush protector. Do not keep lots of brushes in one cup. They will rub together and spread germs.
Wash your hands before handling your toothbrush.
Wash your toothbrush before and after every use. This constitutes holding it under running water and rubbing your thumb over it with force. Do this for five to ten seconds.
Deep clean it occasionally, by placing it on the top rack of a dishwasher and running it with ordinary dish soap.
Replace your toothbrush every three to four months. If it is electric, replace the head every three to four months.
Always use toothpaste. This will also help keep it clean.

[edit] Tips

If you notice the ends of the bristles bending, then it is time to replace your toothbrush.
Consider spending about $20.00 on a UV toothbrush cleaner. It is safe and it automatically shuts off.
By storing your toothbrush in a 3% Hydrogen Peroxide (H₂0₂) solution (changed daily, as it turns to water in a matter of hours) you can keep your toothbrush disinfected.
You can also pour some mouthwash (like Listerine) that contains alcohol into a small cup and stir it with the bristled end of your brush for thirty seconds. The alcohol will kill off most of the bacteria.
Some sources such as the papers cited in external links below strongly suggest keeping your toothbrush as far away from your toilet as possible. And simply putting down the top lid before flushing cuts down the airborne bacteria from waste matter by enormous amounts. Other sources, such as the TV show Myth Busters, claim that the fecal germs are just as prevalent in the rest of the house as next to an open toilet.
If anyone in your home gets a contagious sickness, throw their brush--and any other brush it came into contact with--away. Their sickness can spread along the toothbrush and onto others.

[edit] Warnings

If you keep your toothbrush in a toothbrush protector, ensure it is dry before using the toothbrush protector. Failure to do so may lead to the development of mold on the bristles. Also toothbrush holders with holes for ventilation and that will help with storage and mold are sold.
Note that toothpaste is required while brushing, as it provides a lubricant to help protect the enamel on your teeth.
Living in an overly sterile environment for long periods of time can decrease your immunity. This does not mean that keeping your toothbrush clean will decrease your immunity, it means that keeping everything sterile can lead to a decrease in immunity.
Depending upon the type of plastic used to make your brush, putting it in the dishwasher may melt it. Always place in the top rack and if possible secure it there.