There are three main parenting styles (not including neglectful parenting). Most parents tend to adopt one style most of the time, although styles may vary, depending on the age of the children and the needs of the moment.
The oldest and strictest form of parenting is authoritarian. Children are expected to do what they are told, without asking questions or expecting explanations. Children who are brought up this way often do well at school and have a clear sense of right and wrong; they work hard and achieve their goals. However, children who are used to obeying are more likely to become followers than leaders and may be lacking in initiative and social skills. They may have difficulty making their own decisions as they grow older, and they may fall prey to negative authority figures.
Permissive parenting is largely a reaction to excessive authoritarianism. This parenting style grew out of the 1950s and '60s, as young adults rejected the totalitarian or dictatorial regimes that had led to WWII. Permissive parents allow their children to decide how to behave and what to do, and they encourage them to follow their hearts. They do not give punishments. Children who grow up in this way are often creative and self-confident. For better and worse, they tend not to conform to conventions. The downside of permissive parenting can be that children don't deal well with situations in which there are authority figures (such as teachers, police, bosses, etc.). When parents do not intervene to stop destructive behavior, it can become entrenched.
Authoritative (as opposed to authoritarian) parenting tries to set a balance between the "demandingness" of the authoritarian style and the responsiveness of the permissive style. Parents set clear rules and expect compliance, but they explain their reasoning to the children and allow them some say in setting goals and defining consequences. People brought up in this way learn to cooperate and to be socially responsible. They tend to be good at problem solving and making informed choices, where there may not be a clear "right answer." This is the parenting style recommended by most professionals who work with families today.