Pros:
- (relative) Freedom from regulation
- A curriculum adapted to suit each child's needs
- The ability to focus on a child's passions, keeping them focused
- Focus improved by lack of distractions
- The ability to impart knowledge outside of "school" - ethics, values, etiquette, etc... that often is left out at public schools
- Religion to be incorporated - or not - at the discretion of the parent
- Improved test scores in many cases
- Sheer flexibility of program and scheduling
- Studies show that homeschoolers grow up to be more self-confident and less peer-dependent (and therefore less likely to give in to peer pressures)
Cons:
- Increased cost, still less than private school - Homeschooling is not generally government funded
- Loss of income - one parent is home at all times, and therefore not generally working (or working much less)
- The loss of "grown up time" for a parent that is at home with children at all times
- Lack of regulated standards (a societal concern)
- Possibility of unmonitored child abuse (societal concern) - there is no evidence of a higher risk than in public institutions
Sources: Wikipedia, Homeschool.com