As you're levelling in Runes of Magic, you're bound to come across a few dungeons. RoM offers a varying number of dungeons. You'll encounter your normal instanced dungeons and raids. But you might also see camp dungeons, PVP dungeons, and dungeon gates according to the RoM website. During your early levels you'll visit the normal instanced dungeon for you and your party to conquer.
Two such instances are the Moongorge and the Barrens Cave. These are both in Howling Mountains and are probably the first actual dungeons you'll enter. There is a Fungus Habitat that you might enter before these. It is near Pioneer's Colony at the Myconid Farm. This is a separated area from the rest of Howling Mountains, but it is not instanced since multiple people and groups enter at once. This is literally a grove full of fungus men with an accompanying quest outside its entrance.