BadMike said "There are a few sites online that describe what a megadungein is. Some characteristics are: you cannot reasonably map the entire thing; there are areas controlled by different factions; there is a backstory to the dungeon that goes back a very long time; etc"
Another poster (named Kreeping Deth) on Facebook said: "Large enough and with enough treasure, interesting places, monsters and factions to support multiple parties of different levels exploring all the time. There's no "winning it," because "cleared" areas always repopulate with new inhabitants. No matter how far you go, there's always more. This dungeon can serve as the basis for an entire campaign for dozens of players that can span years and years. Some people like elaborate backstories for them, but that's less important to me because I think that ultimately limits the scope and constrains creativity. It's OK for the origins of its creation and development to remain a mystery.
- chainsaw "These are both viable answers.
A couple of bloggers that I read have attempted to answer this question as well (links to their discussions):
The Angry GM
With that background, on to MY criteria:
1. It can never be fully explored or mapped. PCs should know that they haven't found everything. There is always a mystery of "I wonder what we missed." Undermountain was particularly famous for this. Castle Greyhawk and El Raja Key would literally move walls around to make this true.
2. A megadungeon must have a theme. Castle Triskelion is about a crazy family's home. Castle of the Mad Archmage (and Castle Greyhawk) is about a crazy wizard. These themes don't show up in every room, but they do show up over and over and over.
3. A megadungeon must have lots of entrances and exits. Without this, it is just too hard to move quickly to new areas. Rappan Athuk is a great example of how these portals can facilitate multiple levels of characters delving the same dungeon.
4. Many areas controlled by many factions is another reasonable criterion. Orcs, goblins and gnolls should be holed up in the megadungeon and willing to negotiate to eradicate the other factions. Without factions, a megadungeon is just hack and slash. That gets boring quickly. Felltower (see Dungeon Fantastic blog above) does a great job with this.
5. There need to be goals in a megadungeon. Often, the GM or the players of a campaign will set these. They can be McGuffin quests, search and rescue, get a particular map or any number of tropes. Just sending players in because its there is not good enough for a long term campaign.
I think this is wordy enough for now. Thanks for reading! Feel free to comment if I am wrong, or am missing something.