Answer:
Depending on the public school district you are applying for, most school districts require an bachelor's degree in elementary education - or related degrees - in order to become a teacher. However, some school districts have Alternate Certification tracks that allow degreed professionals from other industries to become certified school teachers. For example, a former rocket scientist with an engineering degree may go through Alternate Certification to become a grade school or subject level teacher (math, maybe?).
If you wish to teach at a private school, the criteria can be completely different. Some require the same stringent certifications (or more) as their public school counterparts, whereas other schools only require a demonstrated ability to teach children without a degree. Private schools, because of this, how differing levels of state certification. Although an uncertified school does not mean the educational quality is necessarily sub-par, because some religious based schools may not seek state certification to remove the government from the business of religious instruction.