I've had a lot of ideas on sieges. I'm a bit of an ancient military buff, so I like coming up with ideas on how seiges could be made more epic and more challenging.
As was said at the start of the thread, the basic ideas for sieges is to starve out the enemy. Of course, doing this to dwarves, who have limitless farms that don't require watering, is pointless. Waiting for the dwarves to die of dehydration would also meet with failure thanks to reservoirs and the like. Of course, the whole farming bit will change in the future, but a having the goblins simply sit outside your fort would both be a waste of time and be not fun. And repetitive.
So I figure what would be cool is to have the sieges vary based upon what bested the goblins last time. Did you refuse to fight and simply ate and drank until they left? Next time they'll prelude their sieges with some spies and dwarven traitors to sabatoge your gates, poison your foods and water, and commit some arson in your farmland. Did you get your water from an outside stream? Then they'll bring some poison and blight the river. Oh, you just use archers to pick them off? Then they'll bring bigger shields and some catapults to smash your archers. But wait, you're sending in some infantry to deal with the equipment? Then they'll build their own fortifications around the catapults and bring some archers of their own. And if a spy detected that your farms are just underneath a pathetic layer of soil? Bring in the siege drillers to drill downwards and raid your farmland. And if they have the pressing need to assault your front gates, they'll soften it up with some missile fire to smash apart your fortifications and collapse your towers. Constant escalation and subterfuge.
I'd also like to see sieges become rarer, but become much more devastating events.