Like 'Powerpuff Girls', all the characters seems to have the same voice after many years. Due to aging, their voices will be changed especially with kids. But how did they get the same voice after 10 15 years?
In the case of the Simpsons, all of the main characters have been voiced by adults, and the same adults have voiced the same characters since the show started.
As for the Powerpuff Girls, many different actors have voiced the main characters. This site shows each of the characters alongside the current actors who voice them. Under those pictures is another link showing how many other people have voiced the role during different seasons. For example, Blossom has been voiced by 6 different actors.
To re-cast a main character, the producers of the show need to audition actors who can mimic the character's voice very closely. Many trained voice actors will have the skill of impersonation, since their voice is their "tool" (similar to the way that a stunt person's "tool" is his/her body strength, reflexes, agility, flexibility, and so on).