Dungeons are where quests take place, bosses reside, and high level gear is obtained from. Dungeons are generally harder than most other content in the game and provide some of the best rewards.
No Instancing
As of the alpha dungeons are not instanced which really sets apart this game from current "modern" MMOs. Whether you are soloing or teaming up with fellow players, the experience is of one shared world which creates stronger social interactions between players.
Looting
Loot on all enemies (except Elites) is also not instanced, meaning once somebody loots a corpse the loot is gone. This can cause a little grief sometimes but keep in mind the loot is plentiful and enemies respawn very quickly!
Consider not burying corpses in dungeons. In theory leaving corpses behind should make them respawn a little slower, which can help when soloing. In a group, please remember that burying a corpse gets rid of the loot. If you don't want loot on a corpse, leave it so another player may loot it.
Trains
Veteran MMO players will remember the infamous trains from classic MMO EverQuest. A "train" happens when a player flees danger in a dungeon, and the enemies chasing the player come in sight of other unsuspecting players who are then attacked. This problem is fairly minimal at present in Project: Gorgon because the enemies don't pursue very far, but be aware that the mechanics allow for it. Don't be angry at other players! It is simply the mechanics of the game, and it could be argued it makes things a little more... interesting. As there is no experience penalty and also no loss of levels in the game (so far), a train will at worst cause your character to respawn in the entrance of the dungeon.