Reading the subject, I thought this was going to be like a gallery showing/explaining the types of fortress shapes that tend to be made.
Like for example (and it would come with picture examples or references from other forts):
Above Ground:
Keep-- Keeping true to classic medieval form, it usually consists of towers and walls in which the people can reside in. The larger towers usually hold nobility, whereas the smaller surrounding towers house military and defenses. The only way in or out is through a front gate with a drawbridge and a moat for further protection
Town-- Just as the name says. Your run-of-the-mill settlement out in the sun. Usually consists of a mead hall, an apartment complex, and some storehouses, along with possibly a market district.
City/Metropolis-- A larger version of the Town. Usually features a skyline of sorts. Usually yields a higher volume of citizens.
Babel (AKA- Tower Fortresses)-- these are generally either massive, or colossal structures that can touch the skies, and then some. You'd think the designer is compensating for something. However, these are more common as a community effort.
Factory-- Make a self-sufficient factory/power station building.
Pyramid/Ziggurat/Dome-- As the name implies; any structure (or a number of structures) that takes the form of the named.
Underground:
"Classic" Mode-- 1 Z-level. Simply put. Sticking to the styles of pre-.28. Channeling is allowed, provided only for flow or as a cut-off from invaders.
Shaft-- These are your common forts that extend from a central column outward and is generally taking advantage of the ease of access. Depending on how the central shaft is designed, it could either be easy to climb, but also easy to die if not careful (nothing but up/downs, or slower to climb, but safer to traverse, with either stepped airways or a corkscrew ramp.
Vault-- Consisting of shafts either formed diagonally or vertically, it usually consists of a series of wide pathways that branch off into smaller pathways leading into bunkers designed for specific purposes. These tend to be the safest in fort designs, provided the flow of traffic and assignment of the bunkers are optimized for quick service. And underground water supply is a must in order to keep these working at their full potential. (SEE: New Wavehandle)
Geofront-- A vast cavern in which settlements are constructed within to house an entire city. (SEE: Undergrotto)
Quarry-Town-- If your main export is stone, or stone products, then you have no need to worry about housing. That literal hole in the ground is your home. Well, there are little holes on all different floors with different purposes of course. Generally carved out in a spiral formation for the main path. Either looks like a crater, rectangular void, or an inverse-drill. Seldom is there a building or structure in the center. Radar dishes or antennae can qualify it as a potential hybrid if sufficiently tall enough.
Ixian/Tleilaxu-- Inspired by Dune; build within caverns, stalagmite and stalactite structures, adapted to house civilian life. Cave adaptation is guaranteed.
(*NEW*) Sin City-- Colonize Hell. Build your fortress in Hell itself. Rumor has it that there's a thriving dwarven fortress in Hell itself. Were they sent there for their crimes against humanity, elfhood, and dwarveny? Hell no, they did this on a whim, and the devil is terrified because he knows what dwarves are capable of; his minions, however, don't seem to learn.
Aquatic/Island/Oceanside:
Pier-- As you would imagine, a functional fortress built atop a pier.
Sandcastle-- Think Keep, except on the beach... with sandstone.
Oceanspire-- Tower, except coming out of the water.
Oil Rig-- A floating structure built atop the water, usually made for drilling into the ocean floor for valuables. Disaters will definitely spell F-U-N for somebody; be it ocean life, or [race]'s life; or a major faction that owns them.
Canal Fort-- A fortress adapted into a canal. Made to manipulate to [race]'s will.
Lost Isle-- A mysterious island with all sorts of oddities throughout with a steady supply of migrants somehow. A megabeast lives here I think.
Sewer-- Qualifies as aquatic due to the fact that usually in fantasy settings, they tend to get unusually large, and have water as a central theme. Usually associated with underground fortresses or beneath most AG forts.
Venetian-- A city/town atop the water. Make sure it's elegant.
Delta Port-- Any of the mentioned built along a delta (if such a map feature can be found; otherwise, they can be manufactured).
Archipelago-- Similar to Delta Port, except with an archipelago.
Sunken City/Atlantis-- If you know Atlantis, you know what to make. Essentially, it's a functional city under water, or built beneath the waves (IE- underground below the water. Have fun with that aquifer.).
Hybrid:
Standard Combo-- Any combination of the A/U/Q mentioned above combined to function together. Sometimes result as a megalopolis if done right.
Cliff-town-- As the name states, these are usually settlements built in/on cliff faces. Examples are few, but these tend to provide some fun in either design or destruction. Access can be from keeps above or below, or a crack in the cliff where a meandering path reaches an external access point to the town. Beware of rigged bridges if this is the case; otherwise *splat*. Usually consists of an entire settlement as a lengthy outcropping from the cliff.
Vines-- Fortresses built like a vine scaling a building. Derived from cliff-towns, they are more like cities built into the cliff, than extending from it; but they usually have a direct route from the base to the top in a single path. Best applied to sheer cliff faces.
Key-tower-- Essentially built as a tower atop a shaft, except a flimsy foundation separates the tower above from the shaft below. Fun times are to be had with this design. Name's as such due to how the tower fits the slot seamlessly like the right key to the right lock. Alternatively, there's a small town in a void that is inversely (as a cavity) exactly shaped like the tower above it. Optionally, there can be protrusions along the top-most portion so Armok can "turn the key". The tower can also have notches to move the tumblers (in this case dwarves).
Hopi-- Cliff-perched homes. How you build them is up to you. Usually made of stone.
Mega-Project:
Shipyard (mega-vehicle)-- Design purpose is usually for a means to build ships for various purposes, be it airship, boat, Titan, landcrawler, or magmaworm. Airships have been attempted, but one has truly succeeded to soar (still moored at site); boats were once a common endeavor with few successes, one is still sailing, though it's fate is unknown; Titans are usually built in a humanoid form, and designed with utility and housing in mind. Considering the scale of effort, and structural stability, these are usually immobile behemoths (SEE: Apex the Immortal); Landcrawlers (AKA-tanks or fortress vehicles) are unknown of at the time, and none have been known to roam the lands; Magmaworms (magma subs), often cast as obsidian vehicles, have been tried, but are commonly ending with disaster. A solution to the matter is still to be found.
Megalopolis-- Monstrous cities built to ridiculous proportions and entirely functional, each with a special purpose in mind. Usually comes with massive temples, production facilities, stadiums... the works. (SEE: Flarechannel, Undergrotto)
Machina-- A fortress which has a primary operation as a computer device of some sort. Designs vary from calculators to data storage, or full-blown computers. Probably the rarest to exist due to the sheer complexity of the construction.
Impossible Architecture-- [insert description here if you can find one], simply: self-explanatory. Quantum fortresses is an example, I guess (Anything that can house an entire fortress in less than 3x3 space.). Adamantine Space Elevator (Or adamintine spire) is a naturally occurring impossibility.
Inverse-scape-- Simply described as a cavern where land once was, and land where sky once was. As if somebody took the time to mine out the floor, only to rebuild it upside-down above it's void.
Hyper-Functional Structure-- Generally a massive structure that not only serves a purpose, but also serves as a fortress that houses an entire fortress. Examples range from dams to bridges to defense networks.
This Looks Familiar...-- A true-to-form replication of known places or things (if going giant-scale); fact or fiction. Not always built to scale, but impressive nonetheless.
Floating Isle/Castle-- Literally a floating chunk of habitable land, adapted to house a town/city atop/within it. Have fun keeping it stocked somehow.
Space Station-- Just as it states. This is a structure built touching the heavens. It must be built in a way that it can operate as if in orbit around the planet. Solar panels can be replaced with perpetual motion machines (water can be the panel part, while waterwheels can process the "sunlight"; alternatively, windmills can take place instead, but in rows (and facing the right direction for consistency)). You should have a means of transferring or making your own food IN SPAAAAACE; and have a fully functional fortress in the heavens. Optionally, depending on what methods you apply in building (whether [CAVE-INS:OFF] or not), you can jettison parts of that station that are rendered unusable or unstable. The real challenge here is getting the material IN SPAAAACE!!!! (Space-walking is encouraged for nobles living aboard.)
The Jetsons-- Ever watch this classic Hanna-Barbera show? Well, ever see any dwarven fortresses operate in a similar manner? Almost everything has to be lever or button/pressure plate operated, and buildings must be built as high as you can make them with minimal support (IE- 1x1 - 5x5 bars holding from houses to entire city blocks), or some means of reaching the other buildings (they don't show the under-city infrastructure (most likely slums), so you come up with something plausible). (For easter egg purposes, make everything out of jet, son.)
(*NEW*)Misc.:
Anti-fortress (Nomad/Gypsy Fortress)-- Build nothing, neither constructions upward (reservoirs/de-salinators are an exception) or mining downward (unless getting materials for anything non-construction, like mechanisms). Just thrive on the surface by whatever means necessary. You can mine and quarry, but you cannot build up or down. I suppose the only other exception is if you find a cavern or carve a small cliff with an overhang, then you can place furniture, but that's the most you can do. Alternatively, just relocate all your stuff into a cavern, and don't construct anything. Wagon always remains.
Microcosm (Nano-Fort Extreme)-- It's essentially a nano-fortress that takes place in smaller than a 1x1 embark space, usually ¼ - ½ the size of an embark square. It must be a fully functional fortress no more than 3Z total, tall or deep, within said space. You can embark in larger than the designated space, just no building past the area equal to 1x1x3 ES in size. For added challenge: Make 100+ dwarves live happily in such tight quarters. Can be done anywhere (AG or UG, caverns, even Hell)
Nice Home, I Think I'll Take It-- Embark in a town, Kobold settlement, fortress, or cave (especially if a creature is living in it), and take control over their home (genocide or hostile takeover) with your embark party. Alternatively...
Kramerica-- Named after Kramer from Seinfeld, just have your embark party live in a settlement (like the listed above), more/less like neighbors and live off their stuff (can't be another dwarf fortress of your making until later versions allow it), while doing your own thing (besides getting your own stuff). You can also sponge off them because you're lazy like that. Let's just hope your neighbors aren't the hostile kind.
Extreme Makeover: Settlement Edition (AKA-- DF Edition)-- Give an unsuspecting settlement, town, or fortress a dwarven upgrade. Bonus points if they were pathetic to begin with, and are living happier (or more miserably) since your dwarves came along.