Let's see... possible king abilities... some of these might work for other nobles instead.
* Royal pardon. Allows you to pardon criminals from the justice screen. Will piss off the cop who was handling the case, and if the 'crime' was offending a particular noble (e.g. work order or export violations), will also piss off that noble. Alternatively, there might only be a limited number of pardons available each year.
* Overrule noble. The king could overrule other nobles in numerous other ways. They could, for instance, force the end of an export ban and prevent it from being reinstated for a while... this would piss off the noble being overruled, naturally.
* Call to arms. The king can summon up military forces from all over the kingdom in times of need. The number you'd get would depend on your relations with the rest of dwarfdom, though, and frequent calls would give you less.
* Expel noble. There is absolutely no reason why the king should have to suffer due to, say, an incompetent or selfishly-demanding mayor. The king can, with a word, strip a noble of their rank and expel them from the fortress. Obviously, there would be consequences for doing this... if you expelled a house noble, say, their house might get pissed... The noble might go berserk instead of leaving. Stripping a high-ranking noble like a Baron of their title might even spark a civil war.
* Grant title. What the king can taketh away, the king can giveth. Or whatever. By signing a few documents, the king could turn any low-ranking dwarf in your fortress into a noble to fill any open gap. This would, naturally, make the affected dwarf ecstatic for a while. Some nobles can't be produced this way... house leaders are probably appointed by their house, not the king, while others might require specific skills that the king can't just grant with a piece of paper. Also, promoting a noble from a particularly unassuming dwarf might piss your other nobles off a little... the lower the person you're promoting, the more upset they'd be. Making a legend into a noble is fine; making a newly-arrived unskilled peasant into a replacement Baron would be much less so. Of course, the promoted dwarf would stop working, too...
* Levy taxes. Just like raising armies, the king can demand regular taxes from the rest of dwarfdom. They can also choose the form they want their taxes in: Coins, gems, food, weapons... whatever. High and frequent demands would not be met well by the rest of your civilization.
[ September 06, 2006: Message edited by: Aquillion ]