So, I have two.  Here they are. 
 
Without giving away any spoilers, I was completing one of the last quests of the game.  This particular quest you can receive in two different ways.  So, I received it from person "A", went to where I was supposed to and completed it.  I think what was supposed to happen was that completing the quest for A meant that person "B" was supposed to hate me and stop working with me (though the quest they were going to give me was identical).  Instead, this didn't happen.  I went to person B and they gave me the same quest that I had already completed, not realizing that I'd already done it.  So I was like, OK, I'll just talk to this dude they want me to talk to and it'll finish the quest.  Nuh uh.  What happened was every time I went to where I was supposed to, the end of the quest would replay (the quest end scripting would initiate and some NPCs would kill each other) and I couldn't speak to the guy I was supposed to speak to because he thought that there was still a fight going on (there wasn't).  I figured this wasn't a big deal (except for the fact that the NPCs have no idea what is happening in the world, the quest scene is glitching out etc.), because I could just continue with other quests and end the game.  Nope.  The best part about this glitch is that, though there were no enemies around, the game wouldn't let me fast travel, because it thought that the quest was still active.  I tried running far away from the scene, and nothing, no fast traveling allowed. 
 
So, I had to restart an early save, but wasn't able to sync person A and person B's missions, so just left person B's mission incomplete.  *Sigh*.  Oh, right, and then I started the last mission and the game crashed.  
 
The other glitch, which I hope someone else has found, is in the train tunnel to the South of Nellis Air Base.  I'd almost finished the game, so decided to go through it, because I couldn't previously on account of the Very Hard locked doors.  Went through, found some ghouls and frag mines etc.  Whatever.  I get to about the middle and there is a room to the right up a staircase.  So, I try to go in but, whoops, I FALL THROUGH THE WORLD.  Ya, just straight down to infinity.  Luckily, I respawn at the beginning of the tunnel, but I think that it is like an instant fast travel, because I kept getting thirsty and hungry.  So, I tried it again and again and there is no way to get up the stairs, I just keep slipping through the floor and falling.  Interestingly, there are a bunch of cans in an infinite loop falling and respawning on top of the hole, falling etc. 
 
I also found a lot of time errors during the Brotherhood missions.  Like, Veronica would be angry because the Elder wanted to stay underground, but in fact, he'd already agreed to leave.

Boone lost his eyes, but they came back when I changed cells. It also crashed once.

hard to understand like that
post with spoilers :P
 
Veronica is not mad at the staying underground part, she is unhappy with the overall Brotherhood policy concerning new recruits and the use of technology. This is the thing that the elder is refusing to change.

Just after getting Ed-E, I went into a night stalker cave and stealth killed a bunch without any trouble and then on leaving the cave, I got mobbed by about 8 of them. Ed-E was already dead before I had control of my weapon and it had already saved because I had save on travel turned on. Every time I tried to reload I got and "Ed-E has died" prompt. Before going in the cave, I walked around the entire area and there was nothing.
 
Later I went into the fire gecko cave with the Legendary Fire Gecko in it and Boone spawned at the other entrance to the cave. I heard a couple of shots in the distance as a ton of them mobbed him and got "Boone has Died". Luckily, I was able to turn around quickly and exit after a reload and it spawned Boone next to me again.   
 
Obviously I have turned off  save on travel. 
 
A couple of days ago, I started everything up and it told me my hard drive contained no save files. I had to turn the 360 off and remove the HD, put it back and restart before I could play my game. I' have never had this problem on any other 360 game before.
 
I've seen a lot of other crazy stuff, but these made me want to quit playing for a while. 

I had an auto-save get corrupted when the game froze on a loading screen.  That's only happened once though in a 40+ hour playthrough.  All the other glitches have been minor stuff like a framerate drop or a texture reloading itself for some reason (only happened twice).

I dont know if I would call it a glitch so much as a game breaking bug, but the DLC error cost me a significant amount of progress.  I checked out Bethesda's forums and found I was not alone.
 
 http://forums.bethsoft.com/index.php?/topic/1135534-how-many-people-have-suffered-dlc-error-and-are-unable-to-load-the-game/?s=33f99718b75d54db725791adf573c468 

Can't load my character.

My freakin' screen turned into a blurry and dimmed mess after i entered and leaved a cave. (happened today, and i got another topic for it on these forums.) I can't find any solutions for it yet...

Had scripting errors on the quest, You'll know it when it happens. 

Lock up when buying and/or selling to a traveling trader at the Mojave Outpost.
Lock up at the Hoover Dam just because I didn't let it load for a bit.

Sometimes VATS makes my screen lose signal so I'm forced to restart. There is also a dud that you can do a barter check over and over to get infinite xp and int check that breaks the virus quest.

Had a ton of issues with people saying things that made no sense at all given the state of the world, numerous missions getting crossed / broken, weapons not being returned to companion characters when leaving casinos, ED-E losing everything she was carrying when she got upgraded, low-light vision being activated at random for no apparent reason, about a dozen CTDs...  
 
Half the time it felt like I was fighting the game itself rather than anything in the game.  There's a lot of superb stuff in New Vegas, and I'm still glad I played it, it's just a shame it's so totally fucked.  The content is so good that it'd probably be GOTY for me if not for how frustrating it became to play through it at times.

My favorite glitch is everyone identifying me as a woman all of the sudden (I'm a dude.)

" I dont know if I would call it a glitch so much as a game breaking bug, but the DLC error cost me a significant amount of progress.  I checked out Bethesda's forums and found I was not alone.   http://forums.bethsoft.com/index.php?/topic/1135534-how-many-people-have-suffered-dlc-error-and-are-unable-to-load-the-game/?s=33f99718b75d54db725791adf573c468  "

Crashed about 5 times. 
My friend, though, got locked out of the Strip and he needs a key to get in.

I had the same problem with the tunnel. My friend had a glitch where his guns wouldn't stop firing.

I have the PC version and luckily nothing major has happened to me. (Yet.)

The worst one I encountered which I was thankfully able to get out of  was the strip gate being locked. All I did was reload a save where I was still on the strip and exited the gate manually instead of fast travelling. WHen I walked up to the gate it said [key required] but I guess because I was on the strip side it let me through anyway. It was never locked again.

There is this glitch that comes up during battle where I cannot perform any action except for movement. This especially sucks when facing deathclaws.

70 hours into the game I'm on the strip finally getting to some of the end game quests. There's a casino I absolutely have to get into. I've been going in and out of the casino the whole game but now when I try to go in the game just glitches. I spend like 30 minutes trying to figure a proper way to fix it. Apparently there is no proper way and seeming as I'm 70 hrs in and headed towards the end I forfeit my end game achievements for finishing the game. I loved the game overall but Obsidian can kiss my ***. (pc)

"The worst one I encountered which I was thankfully able to get out of  was the strip gate being locked. All I did was reload a save where I was still on the strip and exited the gate manually instead of fast travelling. WHen I walked up to the gate it said [key required] but I guess because I was on the strip side it let me through anyway. It was never locked again. "

Had the autosave get corrupt on the loading screens a few times. Just save early & often to dodge this as well as trying to remember your steps when having to reboot the game from a save.  
 
Also another strange pair of bugs, if you have the classic DLC pack with the vault canteen & weathered 10mm pistol, there's a missing art asset I'm guessing, because once I put the 10mm pistol laser scope on it, when zooming out to see the character in 3rd person I have a floating ghostly 3`x3` red square with a white exclaimation point cutting through the middle of the character.    
  
#2 was on the last step of birds of a feather quest in the abandoned warehouse, after the grenade/signal went off I found that at the end of the battle there's one NCR soldier running back & forth among the large boxes in one part of the warehouse. At the end of the fighting there were 2 legion soldiers unconscious & thought they were going to be taken captive or something. I go back to the warehouse to collect the rest of the gear unlooted as I just had one follower with me. Inside the warehouse are the two now conscious legion soldiers just standing there. As I'm still neutral/liked by both sides & early on in the main quest they're just standing there.

All kinds of ill-timed lockups at the end of the game...and two save corruptions. I'm on the 360.

I had minor bugs here and there until today, when my entire fucking game was basically ruined. 
 
I had been advancing through some of the different faction quests, stopping at points where it was obvious I would piss off the NCR (I was trying to side with them - democratic republic yo). When I was ready, I started going through the NCR endgame quests, happy with the choice I'd made. 
 
When I completed "You'll Know it When it Happens," the NCR quest trail just stopped. Some of the NPC's continued to act as if the ending of that quest had not occurred yet. After some web searching I discovered that any hope of finishing the NCR quests was gone, apparently because of something unrelated I had done about 8 hours prior. I still had an old save, and could have gone back to it, but I would have lost the last 8 hours of work when I was already pretty close to the end. F that. 
 
So I finished with an ending I didn't want, completely killing my excitement about the end of the game. I'd had 50 or so hours of fun before that point, but that scripting bug just killed it. Fuck this game. 

was waiting desperately for the latest patch so i could get ED-E back, i had somehow lost him in vault 22. 
new patch comes and i can see ED-E on the world map now, only he doesn't exist in the actual world. 
 
had to finish up the game with only one companion.  
 
 
 
*spoiler" 
ending i chose, siding with Yes Man, i thought i would be in control of all the robots. i was going to set myself up as ruler. thats what the quests hinted at allowing. 

then Yes Man all of a sudden says "im going to reprogram myself to take control." WTF? i might as well have gone with mr. house. 

After giving a quest item over, The screen kind of went dark, loaded back up and i was stuck just standing there.

"After giving a quest item over, The screen kind of went dark, loaded back up and i was stuck just standing there.

                   

                "