Which NPC in WoW will try to kill you and which will not?

The first thing to look for is if you could attack the NPC (move your mouse cursor over them, if it's a sword you can attack them, if it's a hand you can do nothing to/with that npc, if it's another cursor you can interact with them in a friendly way). If you can't attack the NPC, the NPC won't attack you.

If you can attack the NPC, the NPC can attack you (back). But not all NPCs are aggressive and will you attack on sight. Some will (with variable distance at which they attack, this is called "aggro range"), some won't. Regretfully there is no way to check if the NPC will attack you on sight or only fight back when attacked.

For most situations you learn by experience what to expect from an NPC. And with higher level your chance to escape if attacked also improves so it's no longer deadly when you aggro an NPC.

Raidri is mostly right, but there is a way to see which will and which wont attack you. If you are using the default Unit frames or default name plates the background/name plate color will tell you certain things:

Red:    Hostile will attack you when you come to his aggro range
Yellow: Neutral will not attack unless you attack him/her/it
Green:  Friendly will not attack you.
Blue:   A friendly player
Orange: Due to your current reputation standing with a certain faction he currently 
        will attack you, but given you improve your reputation with given faction will
        turn yellow and then green.

Those are the most common ones and I cannot recall any other colors right now. Also most tooltip addons and default will show the name in color regarding hostility.

Hostile npc:

Friendly npc:

Tooltip of Friendly npc:

Here is a picture I found on google demonstrating how it shows up on nameplates:

_{(source: wowinterface.com)}

As you see the yaungol are red = will attack you when you reach aggro range and the turtle is yellow = will only defend if you attack.

E: Neutral cities(Shattrath and Dalaran) are areas known as sanctuaries which are exceptions here is what Nate wrote regarding the subject.

Nate Kerkhofs wrote:
Dalaran is indeed a neutral city, and ALSO a sanctuary, which means that there is no player versus player combat possible (opposite faction NPCs are included in PvP combat). There are some quests that require you to kill NPCs in certain sanctuaries, but you cannot attack the opposite faciton in a sanctuary. Mouse over the target: if you get a sword, they'll attack you. If you get something else, they'll ignore you, since you can't attack them back and it would be incredibly unfair for them to attack you.