To me, the only persuasive argument against the monarchy is that it is the pinnacle of a class system that has no place in our modern society. However, that class system is slowly eroding beneath them anyway and, even if Charles shows no signs of being a modernizing monarch, it is clear that William will be.
Arguments in favour of republic do not persuade me. An executive president like Obama in the USA or Sarkozy in France is a political, and therefore a divisive, figure. The Head of State should be a unifying symbol of the nation, not a divisive political one. And a non-executive figure, like McAleese in Ireland or Christian Wulff in Germany (who I had to look up ... anyone ever heard of him? I hadn't) ... well, what's the point? If you're going to have a ceremonial figure, why not have someone whose family history is woven into the very fabric of the nation? The alternative, it seems to me, is either a washed-up ex-politician, or, worse, a celebrity. Katie Price for president, anyone?