How to find out what workshops are cluttered

Your fortress really only needs 3 things: Food, Fun, and Fermented Beverages.

Food

Dwarves need to eat to survive (duh!). If there is no supply of food in the fort, dwarves will quickly stop doing any assigned jobs as they attempt to hunt vermin to survive.

Dwarves aren't happy when they're forced to eat vermin. A farm of plump helmets is a good way to stave off hunger indefinitely, as long as you have seeds to plant. If you don't cook plump helmets, they will leave seeds when eaten, allowing infinite sustainability.

Booze

Take a gander at any one of your dwarves' profiles. See that last line? "and needs alcohol to get through the working day". It's that important. Every single one of your dwarves runs on alcohol.

No alcohol means unhappy dwarves who are forced to drink water. If they can't drink water, they'll die of thirst. You cannot rely on your stocks screen alone to determine if you have enough booze, because dwarves have one (and only one) rule of drinking -- you can't drink from the same barrel another dwarf is currently drinking from. You may have 200 units of alcohol in your fort, but if all of it is stored in a single barrel produced by your legendary brewer, you'll lose dwarf after dwarf as the line for the barrel gets longer and longer.

So there's two things to keep in mind for sustaining alcohol levels. First, production, which is easy - simply brew the plump helmets you've been growing to eat -- they are a very versatile mushroom. You'll even get the seeds back.

The other thing you need is enough barrels to store the booze. This usually means wooden barrels from a carpenter, but you can make metal barrels as well at a forge. And, recently, stone pots, from a craftsdwarf workshop fulfill the same function. If you don't have excess stone for as many pots as you need, you're a) not digging down far enough, or b) stuck above an aquifer.

Happiness

If the excrement starts to hit the rotary device and dwarves start dying off, your ability to recover is tied directly to your dwarves' collective happiness. If too many dwarves become severly unhappy, you risk a tantrum spiral that culminates in the death of your fort. I'll simply quote from df.magmawiki 's page on Tantrums:

Dwarf A, a craftsdwarf, gets the urge to build a mysterious construction, but unfortunately there are no 'body parts' or shells to be had.

A goes berserk, kills dwarf B, and wounds dwarf C.

A is then struck down by dwarf H, making an unhappy thought for A's friend dwarf E.

B's loved one dwarf D, and friends E and F, get a strong unhappy thought.

D, going to help C, throws a tantrum.

He kills C in his rage, giving another unhappy thought to C's friend F.

F, now horribly unhappy from the death of two of his friends, throws a tantrum destroying E and D's beds.

E, now very unhappy from two of her friends dying as well as losing her bed, goes melancholy and commits suicide by jumping down the well, giving an unhappy thought for D and J; and contaminating the only water source.

D, despite the happy thought for fighting (and killing) C, is overwhelmed by unhappy thoughts and tantrums again.

This time he destroys a bridge, drowning F in the moat (as it has no ramps), and then punches dwarf G.

F's friends, I and J, both get an unhappy thought.

E's body rots, causing J to tantrum. He punches G, hospitalizing him.

D once again punches someone, this time I - cutting his lip.

Without fresh water, G dies a slow death of dehydration.

I, even more angry due to being punched, punches D back.

D, finally being overwhelmed, goes stark raving mad.

I, angry about being D's punching bag, punches J, and J punches H out of anger.

I, Unable to wash his lip with clean water combined with all of the rotting corpses, succumbs to infection.

D dives into magma, creating a unhappy thought for D's friend, H.

H, in the wake of death and Miasma finally goes berserk and finishes the fortress off.

The more happy thoughts dwarves have, the less they care when their lover / child / bff dies a horrible, horrible death.

Luckily, Dwarves are simple creatures, and it is relatively easy to keep them entertained. The wiki even has a page dedicated to this.

A quick suggestion would be to flood your dining hall with statuary and decorations, give each dwarf a bed of their own, and don't let them go hungry or thirsty.

Goblins normally follow their squad captain, if he is alive, unless there's a dwarf within about 20 squares. Squad captains normally charge your base if they can find a path, trapped or not, to a dwarf, and their squads follow. (Note: the previous answer is incorrect; goblins are just as omniscient as you are, except they can't see traps.) However, a known bug right now is that goblins with flying mounts sometimes get confused and have a hard time pathing; this especially affects captains because they're mounted more often than the normal troops. If the captain's mount is confused, his squaddies will just stand around guarding him, rather than attacking on their own. This is similar to the problem that causes attackers to hang around your entrance rather than heading farther in: their captain is caught in a cage trap, but he's not dead so they just stand around rather than leaving him behind.

How to diagnose this: First, find the goblin captain on the units screen. He's the one marked "Elite" or "Master", and he'll probably have a different weapon from his squaddies. Zoom to the creature, and see if he's inexplicably floating above the world, especially if he's above a tree or something. If so, you'll have to order the militia out there, because that's the only way you're going to get rid of them; and you'll have to gain some height so that your marksdwarves can shoot at the captain, remembering that they can't shoot upward. You might have to build a small tower nearby to arrange this. An goblin master bowman stuck atop a tree with no higher ground nearby is a deadly threat, almost impossible to get rid of, because he shoots any of your masons who try to build a tower for the marksdwarves to stand on (and master bowmen are ridiculously dangerous).

If the captain's just parked on the ground, with his buddies, and not attacking you, something else is wrong: probably there isn't actually any way into your fortress. Check the doors; besieging goblins won't path through locked doors or raised drawbridges. Trolls path TO these obstacles because they're building destroyers and they like to destroy them, but goblins care only for dwarves. So go ahead and open the gates. Just make sure the militia is standing behind, and your civilians are burrow-restricted not to go outside, &c.