the dungeons in GW2 are more mechanics-oriented than other MMOGs, and that's likely at least partially due to the lack of the holy trinity. This does not, however, mean that no dedicated healing is possible or warranted in GW2. You'll still want at least one person who can act as a designated tank, another who will heal, etc. The difference is that any class can fill those roles and they will still need to contribute damage. The first time you go into a dungeon's story mode (story mode is required before you can do explorable mode, by the way) you can expect a couple of wipes possibly by non-boss "yard trash". You will likely find traps that can bring you down with one little mistake. The bosses will offer relatively complex mechanics and if you attempt to roll right through them you WILL wipe.
That being said, dungeons can be awesome experiences. I believe that dungeons are where a person truly learns how to play their entire character, which is completely different from the way that other games' dungeons force you to play one specific aspect of your character. I strongly suggest that you bring a couple of weapon sets (unless you're an elementalist and maybe even then) and be prepared to switch up your traits/utilities to deal with the changing landscape. ANet built dungeons so that even the standard mobs are a challenge. As an elementalist in Ascalonion Catacombs, I had to swap between all my attunements but I primarily stuck with Water because I decided to be the primarily healer (yes, everybody still had to use their own healing - I was there to supplement and augment it). Some of the encounters will be melee-heavy, while others will offer seemingly endless flows of mobs, while others will all but demand a ranged solution (and offer melee classes some items to allow them to help). You'll want to keep in mind that everything in the dungeon was put there for a reason. Depending on your group makeup you might not need to use the item(s) but at least take a moment to try and determine why it is there in the first place - it could save you a wipe and repair bill.