Types of dungeons?

Thinking about level design, I've realized I don't have many types of dungeons in my game, and it sort of bothers me because I committed myself to create a world that could be interesting to explore.
There's the forest, the underground cave, the cavern inside the mountain, the canyon, and other "natural" dungeons, but I can't come up with many man-made dungeons except for sewers, prisons and strictly story-related buildings (not really dungeons though).
I love crawling trough cool looking dungeons/temples, but I am adamant about not adding religion(s) in my game just to have an excuse to put pretty temples to explore.
And I hate nonsencial other dimensional bullshit of doom.

Any suggestions or thoughts to share?

Well, there's a lot to consider here. What function does the dungeon serve? Is it a cave where local creatures have taken up residence, a hideout for some bad guys, or a ruin of a past culture? If you're looking for a "hey, look what I found" kind of dungeon, chances are good that it' an abandoned mine or natural phenomenon. Oftentimes you can put in some kind of fringe element of society in a cave or abandoned structure with some verisimilitude intact.

Whether it's vital to story progression or not, regardless of the type of structure, if the player has encounters there it's a dungeon. Don't be afraid of stuffing a dungeon with the unknown monster that has little to do with the actual srotyline, it makes for a nice departure from the grind. Put a nifty treasure in there that is unavailable elsewhere. Just keep in mind, all these places exist in the game world for a reason. Invent a good reason, and type becomes less important. 

Except a few exceptions such as a prison and other buildings and an headquarter (which aren't proper dungeons as I said), the purpose of the dungeons would be mostly to dilute the story breaking it in smaller parts, to add pacing, and minor dialogues. Not all are going to be mandadory to explore to complete the main quest though.
I was planning to add a ruin of a past culture (I'm a sucker for this ), but it's relatively late in the game, so there's no point in worrying about it now.

Okay, then, what I'd do if you really want some man-made structures to explore is use a bad-guy hideout for several of them. Nothing really major in terms of villians, (although you could, see later) but an outpost of heavies that terrorise the local town or something. Wood buildings, a stone command post built ito a cliff or a shell keep, nothing bigger. That way, the adventure into the dungeon is self-contained and has a defined boundary.

Alternatively, since you intend to have several of these dungeons, you could have the "boss" or leader of these dungeons be a lieutenant of sorts for the main antagonist. If you do that, you could use thm as recurring villians who reemerge at endgame as more powerful incarnations of themselves.

As far as the ruins go, consider using them as a "side-quest" location, a kind of uncharted bonus location that is not mandatory to the storyline. That's where many designers like to stuff powerful, unique creatures and treasures, and that give the player a sense of accomplishment for finding them. The problem is, once players find them, they'll be going all over looking for them, so be prepared to put several in.

recurring villians who reemerge at endgame as more powerful incarnations of themselves

With several wings on his back l0l.

Thanks VulcanM00s, you gave me many inspirational things to think about.

Probably rendered redundant by M00sey but:

1. Is the dungeon optional? Storyline dungeons tend to be more grandeur, whereas filler dungeons (normally optional) are pretty similar or plain.
2. Is it super special secret? in which case, you may want to consider making it special or interesting, like, a secret dungeon made of CAKE!
3. How long is it?
4. Does it change as you progress? Harder enemies, darker, scarier or more bizarre surroundings help to tell a player how far through they are.
5. Will you be returning later? Are there areas you won't be able to exlore till you get a certain skill, item or character?
6. Why does it exist? Give it a story, some sort of reason for it to be there! If it's a prison, who or what was kept there?

Some unique ideas could be: An abandoned zoo, a shopping center, army or tactical base, an overrun farm, a town consumed by a forest or jungle, an underground city, theres so much potential here!

5. Will you be returning later? Are there areas you won't be able to explore till you get a certain skill, item or character?

I didn't actually think of this possibility, where some areas are inaccessible until a certain event.
Thanks Grace, I love coming back to places and discovering new zones previously not available (:

Oh hell yeah! We all love game with replay value, players love areas with revisit value!

And cake dungeons.

Purely natural areas with no major landmarks in them are rarely interesting dungeons.  In fact, they're often so uninteresting and mundane that one might wonder why they were included as dungeons at all.  If there's nothing notable there, why can it be entered?  Why isn't it just part of the world map, or omitted entirely?

Make sure every area has major notable features that are unique.  Swamp?  Boring.  Swamp with a half-submerged temple in it?  Somewhat better.  Swamp with a half-submerged temple in it, where cultists have set up camp within the ruined buildings, and erected a massive magical purple crystalline spire in another non-temple section of the swamp to resurrect an Elder Demon, which has turned the earth around the spire black and is sending a stream of constant energy into the sky?  Now we're getting somewhere.

These sorts of things don't have to tie into the main plot.  It helps if they at least fit the overall theme of the main plot - the above example would be great in a game where the plot struggles with the morality of demonic magic (like Warcraft), but not so good in a game where the plot is centered on freeing an oppressed nation from a totalitarian empire (like Final Fantasy 6).

The area doesn't actually have to have any plot at all though.  There's no need for significant dialogue, necessarily.  Even if you don't have the time and resources to make complicated cut scenes, it's still a great idea to make landscapes that are interesting.  Anything that can be described as "a plain <x>" is not going to hold the interest of your players for very long.  Put in some landmarks, combine two or three motifs into a single area, make it memorable.

I help run a free online [link=http://uossmud.sandwich.net]Squaresoft fangame[/link] where we have areas based on Final Fantasy 5, 6, 7, Chrono Trigger, and Secret of Mana.  This is partly a shameless plug for my online game, but those old SNES and PSX games are some of my favorite games of all time and are full of great examples of what I'm talking about.  When you went across a mountain in FF7, it wasn't just a mountain, it was a mountain where broken train tracks led from an abandoned mako reactor, past a burnt-down village that was destroyed when the reactor malfunctioned, to some cliffside slums where the village refugees had gathered around the entrance to a theme park.  When you went across a mountain in Chrono Trigger, it was floating in midair, with massive chains tying it to the ground to keep it from floating away, and little pieces of it had come loose and were connected via their own smaller chains that you could walk across.  When you went across a mountain in Secret of Mana... okay, Secret of Mana had a crappy boring mountain.  The Temple of Darkness was there, but it was just a little generic-looking cave entrance.  It should have been a massive black cathedral or something, with bats circling around it.