The Animal Crossing wikia has a nicely worded paragraph on
this page about tree placement in relation to successful growth:
"Trees must be planted in the center of a 3x3 square of land that does not contain any other tree saplings or impassable objects, with the exception of bushes. Trees will also fail to grow if there are already too many saplings and trees in the vicinity. Trees that fail to grow become wilted saplings the next day, which then disappear the day after."
Trees can't be in the shadows of buildings, on cliffs (I'm fairly sure), or next to any part of the outer limits of town.
Also relevant: I had forgotten the rules for planting trees and planted an apple orchard but the next day all I got was a graveyard. Very tragic ;^;