Worth also noting that if you are Downed and manage to kill a monster/player, you get back up.Death: Its a little complicate (to explain)...
Before dying, you go into a 'Downed' state in which you have a few special skills (replacing your current skills). These may allow you to recover some health, divert a mob, or defend. (Downed skills depend on class.)
If you dont recover from being downed, then you die and take equipment damage.
At this point, you can do a full rez at any waypoint that you've discovered. There are no corpse runs. Waypoints are the general teleport means of traveling and generally not too far from where you died. (Couple of minutes run max.)
While downed or dead (before you rez at a waypoint), other players can help you recover. People are generally pretty good about doing this, its one of the informal social things the game promotes. However, they may choose NOT to rez you in the middle of a battle -- since there may be too much risk (I've been killed several times trying to raise people in a tight battle). If thats the case youll usually get a rez after the battle has died down a bit.
BTW, even if no one's around right when you die, you may still get a rez. Downed and dead players are shown on the map, and its not uncommon for someone to detour a bit to raise you.