The only thing you'll need to actually form a party for are the 5-man dungeons. Those are optional, but are quite fun and are part of the whole experience (plus, lots of very cool and useful gear to get in them). Otherwise, you can roam the game world and play with whoever you bump into and have spontaneous adventures together since nobody is fighting one another for advancement. World Events and everything, all available to you.
One blogger at Kill Ten Rats mentions he strives to
play GW2 like a Kung Fu Master;" I wanted to just walk Tyria to create adventures as I went, you know like Caine from Kung Fu. Guild Wars 2 supports this playstyle. I want to be present in the game world. I cannot stop to smell roses if I dont even notice the flowers."
Pretty much just wander around and have a good time exploring, fighting for the right and following your personal story. Nobody else really intrudes on your experience unless they're naked and dancing, wearing hot pink armor or have a goofy name like "R O F L C O P T R". That's as far as they can affect you, really.