Did some research and found out that the best way to clean your toothbrush is to run it through your dishwasher every few weeks. Who knew?! **It's best to put it on the top rack, though, so it doesn't melt from the heating element at the bottom.** The dishwasher will sanitize your toothbrush.
Other ideas include soaking the head of the toothbrush in boiling water for a few minutes, or in Listerine. There's also a company that makes toothbrush cleaning tablets (kind of like denture cleaning tablets) ~ which I've used before and they work great. But heck, the dishwasher is free. :)
Another tidbit I thought worth mentioning is that it is not such a good idea to store multiple toothbrushes in one cup... They tend to touch and spread germs (ewww...). We used to store ours' all together and it finally dawned on us why we were always sharing each others' sicknesses. Yuck.
So, to keep your family healthy (or, at least, healthier), store toothbrushes so they don't touch, and run them through the dishwasher every few weeks or when someone in the family has been sick.
And, of course, as your dentists says, you should replace your toothbrush every 3-4 months.