This debate surfaces on a pretty regular basis in the UK, and there's been a lot of Royal stuff going on recently, so it's been fairly prominent.
I don't believe the Windsors do as much damage as people seem to think. Yes, they live off the taxpayer, but so do MPs, and all the thousands of unelected aids and advisors and associates to MPs that we never seem to complain about and who actually have a lot more influence in how our country is run. Incidentally, virtually all of these behind-the-scenes officials we never get to hear about are from well-to-do families and have either bought or humped their way into the houses of parliament, without any electoral input from the public. They seem like a much bigger issue as far as taking up taxpayers' money is concerned.
To me, the royal family seems like an entirely inappropriate thing to get angry about. I think the problem is partly that they seem quite rich, they own a few farms and stately homes and such, but this is a tiny fraction of those owned by some of the other, less high-profile aristocratic families we have. As far as the aristocracy goes, the royals are at the top in name only. Aside from anything else, most footballers are richer than the royal family, and people literally climb over each-other to throw their money at them.
One day I expect we will get rid of the monarchy, but the taxpayer will never feel the benefit, any money that was saved will, at best, go straight into the parliamentary budget, and at worst it'll fall into some bureaucrat's pockets. I'd much rather have some silly, doddery, inbred old royals than see some pencil-pushers get richer.
As always, Stephen fry says it better than I ever could.