My two pence - don't abolish the monarchy, let them keep their legacy (and the vast quantities of money and property they currently have, I suppose), but:
a) They shouldn't leech off the taxpayers. They're filthy f*cking rich, they neither need nor deserve the money.
b) They shouldn't have any influence over politics or military, officially or otherwise - this is supposedly a democratic nation.
Most people I know are sensible enough to see it from a similarly reductionist standpoint as I do - it comes down to whether you think a person deserves to be given a free ride their entire life, with all the money they could ever want or need, supplemented by people poorer than them, just because they had the sheer, dumb, blind luck to have been squeezed out of a specific woman's tubes. A woman whose only notable feature is that she had the sheer, dumb, blind luck to have been squeezed out of a specific woman's tubes, and so on with similarly arbitrarily-assigned people, going back centuries until you find some random dude whose combination of skill, ruthlessness, resources and luck allowed him to seize power (now that guy I might find a small amount of grudging respect for). And all they have to do in return is wave at the plebs now and then (maybe even shake a hand, but don't remove your glove - peasants are all filthy, disease-ridden curs, being poor must be infectious or something), cut a ribbon on occasion, and try to avoid making a scandal. And that last one is kinda optional. Their qualifications and the vital service they contribute to society are surely on a level with doctors who heal our sick and wounded, scientists who advance our knowledge, and police who maintain order.
The fact is that in any just and democratic society they should just be regular citizens - no dipping into public funds, and no rights or privileges beyond those also possessed by John Smith from Scunthorpe, you know, that funny-lookin' dude hunched in the darkest corner of the pub. And if they balls-up their finances - well, that's their own damned responsibility like the rest of us, and it'd be time to get a damned job like the rest of us. They still have enough friends in sufficiently high places to walk into a 6-figure salary based on naught but nepotism. And if they don't like policy x, that is currently being discussed in parliament, they should write a letter to their local MP (the response to which will most likely dodge the issue and answer a question you didn't ask), like the bloody rest of us. But then, some people are more equal than others, eh?
Ah, feels good to get that out. [/rant]