Taken from cutebonsai
Some guidelines on which branch to remove or to keep.
1. Branches (called "yagome") growing from the bottom of the tree.(Yagome is just a sprout first but when it becomes a branch (yagoeda), it takes all the nutrition and can kill the other new growing branches on the tree.)
2. Branches (called "kan-nuki eda" or "boat") growing at the same height on the both sides of the tree and one of them should be removed
3. Branches crossing the trunk.
4. Branches growing close to each other and are short, of the same length and in the same direction. (ruins the space that makes good bonsai visual form.)
5. Branches (called "dou-nuki eda") growing from the middle of the trunk. It blocks good growth condition.
6. Branches (called "tachi eda") growing straight up.
7. Branches (called "sagari eda") growing straight down.
8. Branches (called "gyaku eda") growing in the opposite way of the branch they are growing from.
9. Branches (called "kuruma eda") growing from the same spot in many different directions.
10. Branches (called "kousa eda") crossing other branches.
11. Branches (called "Tochoshi") growing much longer than other branches. (however, this branch is sometimes used to adjust the growth of other branches and/or growth of the trunk for the purpose of making the trunk and other branches thicker or to slow down their growth.)
12. (Not pictured) Branches pointing at the viewer from the front side of the bonsai. (this is because pointing at someone is considered to be rude in Japan. No exception even for bonsai I guess)