Basing this thread off of an interesting thread posted in the Elder Scrolls section, I thought I might as well create a spin off in the Fallout section to get some more bizarre answers from people who play New Vegas, I'll start.

My first death ever in Fallout New Vegas was after defending Goodsprings from the Powder Gangers attack, I ventured up to the graveyard, By this time, It was the dead of night, So, Of course, I seen the Strip, Believing I could get there in around 20 minutes, I decided to head that way to start off, Within a few minutes, I was savaged by Cazadores, And all I had to defend myself was a few sticks of dynamite and a crappy 9mm pistol, Safe to say, I was killed in a few seconds by their OP venom

My REAL first death (One that was somewhat fair) was in the REPCONN facility for the mission you get in Novac, I want down into the basement, Not detecting anything with my Perception, I immediately bolted into the corridors, and was jumped by Nightkin with Rebar clubs, I never screamed so loudly in my life before, And from that day forward, I sneak around where ever I find Super Mutants and VATS spam, So I don't make that same mistake (And noise) ever again.

First death was actual a deathclaw, trying to get to new vegas is bitch but a deathclaw oh boy!
I had to travel by rock beside black mountain, it wasn't easy but i made it!

My first death would be when I tried heading straight for new vegas instead of doing all the quest line that leads to vegas. I decided to go into the deathclaw quarry and try to clear it out but I managed to get massacred because I wasn't use to the changes new vegas made.

Honestly my first death was just starting the game and trying to kill Victor,I thought i could take him but in the end it was he who rolled around after the fight. It made me pretty sad

My first death was after leaving Goodsprings, I took the road north, I then ignored and skipped through the warning... Those darn deathclaws man.

My first death was to cazadors because I was the badass courier who survived a bullet to the head and some flying insects should be no problem. Maybe fighting them at level one was a slight miscalculation on my part.

I was level 1 or 2, had just reached Primm. I had earlier killed a Powder Ganger, they attacked you for no reason before later patches, but either way: I went into one of the NCR tents, looted some NCR armor, tried it, dropped it because it was too heavy and put on the Powder Ganger armor.

As soon as I stepped out of the tent into the NCR camp, wearing Powder Ganger armor, I was gunned down immediately. From that point onward wearing faction armor has slightly bothered me.

@Sierran
I can relate. I was sneaking around there looking for Harland's friend, and there's nothing anywhere, but suddenly the sneak meter thing says [DANGER] and the battle music starts playing, I look around, paranoid, and after about 2 seconds a stealthed Nightkin bashes my head in with the Rebar Club in one hit (I didn't have full health and I was very low leveled, not expecting to fight Nightkin)

My first death was when I was walking through Quarry Junction, over encumbered, and level 5 lol.
I thought had the most OP weapon in the game the Guass Rifle.. I felt like i could kill anything after killing baby Deathclaw then the Mother came and I got completly detroyed by her. No more going into
Quarry Junction over encumbered for me..

The cazadores north of Goodsprings. I knew Fallout loved making you follow a specific route with superpowered enemies everywhere except where you're supposed to go, but I hoped NV game would be different and not punish free exploration so harshly. I was mistaken.

Well lets see, I did not think it was neccessary to go the long way to get to vegas. I wanted to shoot some bitch ass benny in the head now. So I travelled up North. Into Scorpion Gulch. Realising I was completely underprepared I ran away from the scorpions, and came face to face with my first Cazador. The thing scared the crap out me. It was fast, it was strong, and It was hard to hit.
After I killed it, Its buddys were soon far behind me. So I ran. I ran so far away, but Then collapsed to the ground. Because I was also wondering why the hell I was losing health. I found out after my second tumble with Cazadors that they poison you with their stingers.
Thats My story of my first death. After that, anytime I saw a Cazador I kept my distance or broke out some heavy damage weapons.

Trying to be the hero off the day in the stand off between goodsprings and the powder gangers.. Worst mistake I ever made, I never got wreckt so hard.

Wait, what happened? Did you get no help from the locals? or did you attack the Powder gangers with your fists?
How'd ya die?

My first death was at the gas station just past novac. I had just ran past the station when some legion guy just ran up to me and said about Caesar marking me for death, this was my very first play through so I didn't know about these assassins. I killed the four guys with about 20 something health left, but then two cazadors came flying up to me from behind the station and attacked pretty much at the exact same time, so I didn't get chance to go on my pipboy to heal

I think i got killed by a Deathclaw when i took the wrong direction and went north of goosprings.

a mine while walking into primm , never taught to look at the ground

It was when I was going to Novac pass Primm and whilst trying to dodge those Vipers I unintentionally hit a mine near a car which set off a chain of explosions and grief.

Heading on the road to the Mojave outpost I thought it would be fun exploring this station, I did not relize the Jackel members waiting to ambush me.

Tried to get into Primm from the wrong side, couldn't find the entrance, got shot to death through the fence.

I didnt follow map markers and ended up in the middle of cazador territory, while being stung to hell I was then finished off by a wandering deathclaw.

I am surprised how well I actually remember my first death in Fallout New Vegas. After I had completed all of the quests at Goodsprings, I decided to make my way off into the wasteland. I passed the graveyard up the hill and went down into the small canyon that was further up and was surprised to see a cute family of giant Scorpions. I was Massacred.