Activities - Every city will have activities that fit in with each unique style of a city. Activities will be games in which you can play at any level as they put everyone on an even footing. Some activities are "hot-joinable" others require you to wait in a queue. Winning activities will net you rewards such as rare skins for armor or weapons. There's about 30 activities in game currently.

Here's the ones we know:

Archery
Bar brawl
Keg Brawl
Shooting gallery
Smash ‘Em Up
Snowball fight

Activities, or mini-games, are events that take part in the capital cities. They are very specific, each activity having different rules from the rest of the game.
Activities can either be solo – where the player competes for a higher score, team-based or a free-for-all. Some of the activities that have most PvP elements are including, but not limited to: bar brawl, snowball fight, keg brawl.
Players can participate in activities regardless of their level as activities are played on an equal footing.
Some activities are hot-joinable and can be entered while they’re in progress (such as the bar brawl).
Activities carry rewards. An example is given of a player knocking someobody out in a bar brawl and acquiring a Tooth (trophi item), which can be exchanged at a collector for various cosmetic items. - OnlineWelten
There are around 30 activities. - GameReactor

Examples on activities:
John Stumme:The bar brawl is, quite literally, all about downing an ale and breaking the empty bottle over someone else’s head. Ales come in several different flavors, each conveying different effects when consumed—for example, Grenth’s Grog goes down easy but comes up rough, allowing the player to belch out a noxious gas cloud. As you might imagine, this burp cloud is unhealthy to anyone foolish enough to get close, as well as unattractive to prospective dates. Be careful when imbibing ale! As characters become increasingly more drunk, their chance to land a critical hit rises… as well as their chance to totally miss with attacks. In the bar brawl, players can choose to throw an ale bottle to stun someone, or use it as a makeshift bludgeoning object. Bottles have a chance to break on impact, but if that happens, the fun isn’t over yet—you can use your broken bottle to shank people!

[…] Kick someone into a table, splintering it into pieces, then send another opponent flying by swatting them with one of the boards from the broken table. Use your surroundings to your advantage! If you see someone else engaged in a fight,why not be the opportunist and chuck a keg at them from behind? There’s no teamwork here; you’re in it for yourself, and just like an actual brawl, you’re encouraged to fight dirty in order to win.

John Stumme: For example, we’ve got an activity in Hoelbrak that’s basically a norn interpretation of basketball, so you’ve got passing, shooting, etc. The only difference is that the ball in this case is a heavy keg of ale.

Energy


Skills no longer cost energy. This means energy potions are also gone. (Sorry to everyone who so vehemently helped us defend their existence.) In place of the energy-potion button is a new dodge button. This allows players to use the mouse to dodge and lets players bind dodge to a single keystroke. If you are moving in a direction, the dodge will take that into account and dodge in that direction. If you are not moving, you will dodge backward. Dodging now also evades attacks, making it a more effective and understandable way to avoid big creature attacks or to get out of AoE spells. Dodging is limited by energy, which regenerates over time.

We have a new long-term replacement for the other benefits that energy potions provided to our system, but since it is not in the game yet, we aren’t talking about it.

Skill Acquisition


The acquisition of skills is changing. Why? Because it wasn’t helping teach people the game, it didn’t fit with how skills actually worked, and it didn’t carry over the fun collection element that made the original Guild Wars unique.

A weapon’s skills are now learned by fighting with that weapon. Because weapon skills are tied to weapon use, there is no reason to visit a trainer and make choices about which ones to unlock. Instead, it makes more sense to learn how to use the weapon by, you know, actually using it.

Non-weapon skills are learned in a different way. The second half of the bar will be unlocked using a collection mechanic similar to Guild Wars. We want players to make fun choices about how they build their character, so the new systems will help promote this. Along with this, the player progression of traits, attribute-point spending, and skill tiers have been updated as well, but the final implementation is not a part of this build either. For this demo, the trait panel is disabled, and when the new system is ready, we will explain how it works.

During an Interview at PAX Prime 2011, our staff got Colin Johanson and Eric Flannum to spill a few details on the PVP system in Guild Wars 2. Not only will ArenaNet be making up their own servers for the quick and dirty PVP matches, much like the shooter genre's setup, but Eric and Colin said they plan for players to be able to create and host their own servers or games with specific rule-sets as well.