The best answer is by inference.
We start with Walk:
Movement: Move a number of squares up to your speed.
Provoke Opportunity Attacks: If you leave a square adjacent to an enemy, that enemy can make an opportunity attack against you.
And continue with an Opportunity Attack:
Interrupts Target’s Action: An opportunity action takes place before the target finishes its action. After the opportunity attack, the creature resumes its action. If the target is reduced to 0 hit points or fewer by the opportunity attack, it can’t finish its action because it’s dead or dying.
The persuasive inference, however, comes from the Fighter's class feature, Combat Superiority:
You gain a bonus to opportunity attacks equal to your Wisdom modifier. An enemy struck by your opportunity attack stops moving, if a move provoked the attack. If it still has actions remaining, it can use them to resume moving.
From the "interrupt's target action" of the opportunity attack and the explicit note that Combat superiority, as a class feature, stops movement, the specific before general rule suggests that anything that does not so have that text does not inhibit movement.
Therefore, as forced movement can happen in the middle of voluntary movement, DMs should encourage players to note the exact path they take across the battlefield. While most of the time this won't matter much (as a safe path exists), the presence of OAs and hidden obstacles suggests this social rule.
-- Edit --
Clarification: looking at the text of move suggests that all movement proceeds square by square, rather than as any kind of path. This suggestion is vague, however:
Whenever a creature, an object, or an effect leaves a square to enter another, it is moving, whether that move is done willingly or is forced. This means shifting, teleporting, and being pushed are all moves, for example.
Thus movement is the act of leaving one square to enter another. As walking may only choose adjacent destination squares (unlike teleportation) all moves must proceed square by square, rather than as some sort of (as @ace puts it in one of his examples) preprogramed route.
Happily, this conception of square-to-square movement also makes sense. Because, in the real world, people can choose to not move somewhere in the middle of the movement to that place.