Suppose I nudge a piece back on to the center of its square using a light tap with the back of my little finger. Will this constitute touching the piece within the meaning of the FIDE touch-move rule?
Article 4.3 of the FIDE rules states:
Except as provided in Article 4.2, if the player having the move touches on the chessboard, with the intention of moving or capturing:
So, if it is clear that my intention is merely to adjust the position of one of the pieces then touch-move does not apply. Of course it must be done on my turn otherwise I am liable to be penalized for disturbing the opponent.
EDIT (2018): The latest 2018 edition of the FIDE Laws of Chess contradict this -
4.2.1 Only the player having the move may adjust one or more pieces on their squares, provided that he first expresses his intention (for example by saying “j’adoube” or “I adjust”).
4.2.2 Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent.
So, if I clumsily brush a piece with my army or knock one or more pieces over this does not count as intention. However if I adjust a piece without saying "j'adoube" or the equivalent then I must move the piece.
Small kids playing with tournament sized sets on school sized tables topple their kings all the time, because they can hardly reach the middle of the board without touching the tops of the nearest pieces by their elbows. When repositioning the fallen pieces they do so silently because the situation and their intention is already clear enough. A silent correction minimizes the disruption to the opponent.
You should say J'adoube when it's not entirely clear whether the piece has to be repositioned, because being explicit about not making a move minimizes the disruption to the opponent.
Minimizing disruption is not only sportsmanlike behavior, but also a good habit to adopt to prevent disputes.
(With the post-2018 rules, I wouldn't risk skipping on saying J'adoube, not even with my king lying on the floor. But I would also not claim opponent's intent if I'm sure there was none. Have fun.)