Well, an ambiguous Sudoku is like a 12 line sonnet...
It isn't computationally relevant but even if trial and error were a simpler approach I feel like that is not in the spirit of the game. Sudoku is a number maze, the goal is to backtrack.
Also I refuse to attempt something that is supposedly too difficult for humans to solve, I'm incapable of quitting puzzles and don't relish spending the next X hours proving it can be done :)
9x9 grid of digits with an ambiguous solution is not a Sudoku. It is part of the definition.
Within the set of initial grids that have unambiguous solutions there are ones which require guessing or backtracking, these are generally not considered proper Sudokus and are not presented to humans to solve.
If a Sudoku has one and only one solution, then it is always solvable without guessing or backtracking. It just might not be within the scope of the human brain. There exist (many) configurations where every cell is influenced by every other, so to solve any one cell essentially requires a simultaneous solve of the entire puzzle. There's no theoretical reason a human couldn't do that too; it's a problem simply of computational capacity not fundamental approach.
They're typically designed to be unambiguous (only one correct solution), so in that sense there is always a 'correct' move.
However, finding that correct move is exactly as hard, in the computational sense, as finding the solution to the entire puzzle.
> . . . | . . . | . 1 2
> . . . | . . . | . . 3
> . . 2 | 3 . . | 4 . .
> ------+-------+------
> . . 1 | 8 . . | . . 5
> . 6 . | . 7 . | 8 . .
> . . . | . . 9 | . . .
> ------+-------+------
> . . 8 | 5 . . | . . .
> 9 . . | . 4 . | 5 . .
> 4 7 . | . . 6 | . . .
There should only be one solution. Enjoy yourself, and remember: No guessing! (Source: http://en.wikipedia.org/wiki/Algorithmics_of_sudoku#Exceptio...)