Great thread. I recall a while back reading Frank Leboeuf (remember him?) talking about his role as a 'cultured' centre back. He said that it was down to playing as a creative midfielder in his youth, but he referred to the role simple as 'number 10' - this being traditional number in France for the position.
I think it's more club-specific in the UK. As someone said, the 9 shirt at Everton is freighted with a certain amount of sentimentality given the number of great players to wear it (we can't claim to be the only club to justifiably exalt this number, though). Man United's 7 has similar connotations.
Sometimes numbers are also simply en vogue for a while: the no. 4 shirt became popular for central midfielders not all that long ago (partly, I think, to to the ever-maligned no. 6 shirt that has always tended to be unappealing for non-CBs).
I'm indifferent towards the personalised shirt numbers these days. I can't pretend seeing Dempsey as no. 2 doesn't irk me a little, but I know that's just because I'm so accustomed to the regular usage of it (and, after no. 1, surely the RB shirt is the most static of the lot? We've had plenty of no. 3 CBs, while 7s, 8s and 11s have all been assigned to strikers. Then there was Donovan's no. 9) and humans tend to be funny with change.