2-loop and 3-loop braids. Fun and quick to do. 3-loop braids make great friendship bracelets, shoelaces, decorative ribbons, strong cordage. These are 6-strand braids, twice as intricate as a pigtail braid. Can be made round, flat or divided (two braids at once).
2-loop braids are even easier--just one move that repeats over and over. Makes a flat, though somewhat curly, 4-strand braid.
You can teach the 3-loop braid to kids as young as 8 years of age if they are interested, and even some adept 7-year olds if they are stubborn and determined. I haven't yet tried teaching the 2-loop braid to young children--its one move, while easy for an adult, might not be so easy for younger children.
Re teaching children: For the 3-loop braid, a child under age 7 probably isn't physically ready to learn it (even if s/he is super-smart, can already crochet, fingerknit, etc!) The index and middle fingers still haven't physically developed enough to work independently. (the fingers work together in knitting, etc, not separately).
It's the same thing for 5-loop braids. Around 10 and a half or 11, kids start to be able to use the ring finger independently of the middle finger. Before then it's just frustrating to try to learn a 5-loop braid, after that it's fun and easy. (This is a physical milestone, not a mental one, it doesn't depend on how smart the the child is, or whether s/he can already knit, etc!)
If a child has been braiding with 3 loops (or maybe playing piano?) for a long time s/he may be able to move up to 5 loops sooner than age 10, though.
Square and flat braids, also how to make a slit in the braid, to be a buttonhole or loop at one or both ends of the braid. Children 10.5 or 11 and older can learn it (the ring finger hasn't developed enough til then). After learning 5-loop square and flat braids, go up to 7 loop square and flat braids. (not the same as the 7-loop spanish braid of my other videos, it has twice as many moves as these braids.) Then you'll be able to learn 9-loop square and flat braids (my favorites!)