Okay, this is a recording of the demo from GamesCom with designers from ArenaNet providing juicy details as we go along. You'll see the dynamic event system in action (the future of MMO quests essentially), along with the combat (some of the best flowing combat I've seen in an MMO) and the personal storyline and how it branches acording to your choices. Finally, you get an epic boss fight! I recommend watching the whole thing if you're enthusiastic enough about it, but I've provided some pointers to the most interesting stuff below the videos. Enjoy!
EDIT: If anyone is interested in more information, you can visit the official thread here: http://gamrconnect.vgchartz.com/thread.php?id=108048&page=1
EDITEDIT: Remember, all of what you see here is comes at no monthly fee! You buy the game, and it's yours to play just like any other normal game you buy. 
There is some presentation to begin with in the first video, background info on the story and gameplay mainly, character creation starts at 5:15 in the first video, actual gameplay starts at 10:30.
From the beginning of the second video, you see some of the dynamic event system at work, finishing off with a big boss battle to mark the end of the tutorial. Right after this, you get to see a bit of how the story branches.
Around 6:00 into the second video, you get to see more of how the dynamic event system works, with some info on the class versality as well.
Around 9:20 in the second video, you get a bit of an overview of the skilltypes in the game.
At 10:45, there is info on how the dynamic events impact the world, from the big things to the smaller ones.
At 11:30, you see a brand new event starting out of the blue, with more information on the impact of events.
At 12:50 in the second video, we enter Divinity's Reach, the human capital and are told how it is build to be alive and a good place to socialize and relax.
From the beginning of the third video, there is a great presentation on the art in the game, beautiful!
At 1:40, you get many details on the personal storyline and how it can change, with some info on the travelling system as well.
At 4:50, the demo changes to a Charr at level 45, so it's much more high level gameplay. There are more details on how the versatile the classes are too, with details on how the weapons change your weapons.
At 8:45, there are a few events happening, with an event chain being visible.
At 10:15, we get to see an epic boss battle with The Shatterer, a big dragon. There is an interesting event chain detailed in this section as well.
