You always need to have at least one space surrounding a tree, so you can't plant it directly next to a wall, a house, or another tree. Doing so will just be a waste and the sapling will wilt and die.

X = Tree O = Surrounding space

OOO OXO OOO

As an easy test, make sure you can run in a circle around the hole that you dug for your sapling.

However, I have found that in this game, you cannot have a tree completely encircled by other trees when you plant them either (can't remember if this was the case in earlier games, but I don't think so), or it will not grow.

In order to avoid this happening, try to initially plant saplings in rows of 2, so you don't accidentally block in other saplings. After these rows have progressed to the first growth stage past the sapling, you're safe to plant another row (but not another 2 rows at once, as the first "new" row would then be completely surrounded again).

Note this spacing. It theoretically should work because each hole has a full space around it, including the center one.

However, the next day, we see that the center one wilted and died. No matter how many trees you try to plant there in the center spot, they will die.

This will also fail even if you use staggered tree spacing instead of straight rows, like in the following image:

In conclusion, basic rules: