Most countries require the prospective teacher to have a Bachelor's degree. This is usually the minimum requirement that governments demand of foreign workers performing an educational activity.
Along with a BA/BS most institutions throughout the world require a basic TEFL certificate. The most widely used certificate is the CELTA (Certificate for English Language Teaching to Adults) administered by Cambridge University.
The best and most high-paying jobs as an English teacher abroad require a second certificate or a masters degree in ESL (English as a Second Language). These positions include school managers or director of studies.
Having an appreciation of foreign cultures is definitely a requirement for teaching English abroad. Teachers are usually immersed in the culture of the host country and must be willing to adapt to the local ways of doing things.
When teaching English to speakers of other languages patience is definitely on the menu of necessary requirements, especially if they are beginner students.