I was thinking about all the different character types that are possible in New Vegas, and I was curious; does anyone think that someone could beat the game without fighting at all? Such as just passing speech checks, barter checks, sneaking around, etc?

Nope.

Yes you can.

Yes but it would take alot of running so as too not kill off the random viper gangs and bloatflies

To get around that you really just have to memorize a path to get around everyone.

You would miss like %70 of the content. And I'm not even sure you can get enough experience to increase non-combat skills to sufficient levels. Oh and final mission is a no go unless you're ok with companions.

Actually yes you can my good sir!
Hire a companion, they'll do all the dirty work, plus you can still do more "aggressive" playthroughs. I have played a pacifist playthrough myself. It is actually much more thrilling, knowing that you can't fight back. If you want ur companions to kill something non hostile, punch it, it won't count as a kill, and your companions still take care of them.

i know it's not possible when your with the legion

Companions fighting is you playing a pacifist but cheating.. same with the Deity awfull KO weapons.
If you start off the game thinking non com is an option.. you have to ignore the actual linear story path that you are set on.
Goodsprings.. Primm.. Mojave outpost ( one non com quest finally here ).. all the way to NoVac, where the option to ignore the combat route finally is shown.
Then you have all the faction quests, no route has not got a path were you don't kill someone.
Then I think of those only two have a way not to kill anyone directly.
Of those paths, only one has it so you can avoid indirect fighting as you try to avoid killing the ones you were sent to deal with.
End quest is all combat apart from two speech moments.

Answer is no, even if you don't fight back combat is certain and often.

Afaik you can, and someone did. http://www.neogaf.com/forum/showpost.php?p=24221124&postcount=9108

it's possible but why would you want to do that?

Roleplaying purposes and for fun.