Don't Panic
Metroplexity can be a little different than the RPGs you might be used to. There's more than one place in the game where an important NPC can die (and they often do). But don't worry! The worst this can do is limit your options a little: you'll never be locked out of completing the main quest. And if you'd like to try again, you'll have the opportunity to do so soon enough.
Contacts
David (& Lo)/[Shard]
After making your way through the abandoned building, you must successfully defeat a rather tough group of enemies. If they win the fight, David is shot. The Beaten Man encounter page has some advice for making that fight easier. You can also rescue David with no risk of him dying - see Joining the Third Eye.
Lo will also die if he is being held captive, but that won't happen unless you told him to go fetch David himself.
If David or Lo die, the quest to rescue him will still count as completed. Two branches of a later quest will be closed off, but you can still complete that quest through the remaining options.
Dr Amundsen/[Saber]
Dr Amundsen is also being held captive, in the Underground Asylum, and if anything, her captor is even more difficult to defeat. The Hall of Doors encounter page has some advice on making that fight easier, though you can also rescue her without any risk of her dying - see Joining the Third Eye.
There are currently only minor gameplay consequences for Dr Amundsen's death. The quest to rescue her will still count as completed, but will slow down a later semi-required quest to a much slower pace.
Carlos/[Gang Boss]
If you ask Carlos to put in a good word for you with the Fangs before you start the Docks quest, and then go on to kill Fangs in their hideout, he will "disappear" at the end of that quest. This (obviously) prevents you from selling him Eclipse on Dr Thomas quest, and also stops you from getting a skill, if you had not gotten it already. So, be nice with the Fangs if you ask to be introduced to them.
Others
The Artist
Killing this guy (or failing to save him, at another point) will get you a unique skill, though it may lock you out of some optional areas or questlines, depending on when you do it.
Boris
Hey, you attacked him! Don't worry, the Russkis probably won't start WWIII.
Dave the Horrible Poet
This hipster will stay dead if you kill him. May cause some of his friends to react poorly to you.
Other opponents that will stay dead if you kill them:
- Boris
- Design Student
- Dr. Johnson
- Dr. Mira
- Force Beast*
- Ghoul King
- Masked Shaman
- Midgard Special Officer
- Ocean King
- Pool Shark
- Silhouette In Flames
- Skittish Bum
- The Hammer
- The Mask/Grasping Hand/Shrouded Hand*
- The Navigator
- The Squatter King
- Vine Confluence
- Warehouse Supervisor
* Conditions apply