In what ways can my game be affected by the actions of other players?

My opinion, but based on all the statements I've read from Bioware:

YOUR changes generally will not effect the shared world. How could they? If you cleared a Stronghold, that would mean that no other player would be able to -- they'd show up to an empty dungeon.

HOWEVER, that doesn't mean the shared world can't be changed. World-wide events, like a big storm (an example they've used) would be seen by everyone. A frozen ice pond could be melted and open up a new area to explore, accessibly only by going under water to reach the entrance.

Server-wide community goals to work together to reach? Sort of. They've mentioned Daily and Weekly events, which may have the window dressing of all Freelancers working together for the greater good of Fort Tarsis, but the reality is that everyone will be in it for the better loot.

Influence of NPC factions? I don't know. I like the idea, but I haven't seen confirmation or denial one way or the other.

What's the point of having "so many" (let's hope) other players online? Absolutely nothing to do with the story, that's for sure. As for gameplay, the more players online, the larger the player pool for matchmaking to work with. That's pretty much it. For you personally, it's a means to an end. If you want to tackle a particularly hard mission, and you can't do it by yourself, and your friends are busy or don't want to join you, you'll need matchmaking to fill the gap. Otherwise, they are an invisible resource you (hopefully!) will be completely unaware of most of the time. As a long time MP FPS player, sounds like heaven to me.

Yeah, thats what I understood from the interviews as well, which is good! I certainly don’t want other players affecting my branching story! So its good that the Personal Story is separate from the “Shared world”.

I just don’t understand what the appeal of having a “shared world” is, if we can’t make lasting changes that are seen by others, or if others’ actions can never affect me unless they are in my party. What you mentioned earlier about big storms and melting a frozen pond sound like interesting changes to the shared world, no doubt, but they are changes made by the developers, not by the players. So they really might as well just be an instanced dungeon for 4 players to enter, except that in between sessions the devs can make changes to said dungeon. =/

You go down more than 2 times within 3 minutes. You're gonna get tea-bagged.

And the more matches you make the better your prospects for MP romance, too.

your the only pug player out of 3 friends, need I say more