Is it possible to play any of the Fallout games in a nonviolently way? If so, could anyone please either give me tips on how to get through various parts of the game in this manner or provide me links to a nonviolent walkthrough?

Assuming you leave out random encounters with rodents, raiders, the mob, etc. it's possible, although I'm not sure about the Military Base in FO1.
Off course this does mean you will have to skip a few quests.
You can check Per Jorner's [url=http://user.tninet.se/~jyg699a/fallout.html]FO1[/url] and [url=http://user.tninet.se/~jyg699a/fallout2.html]FO2[/url] walkthroughs (scan for diplomatic).

It is possible to finish fallout 1 killing only the last boss, it has already been done. Not sure about F2 though.

You don't have to attack anyone in Fallout1. Just search youtube for the fallout speedrun.

That depends on how nonviolent you want to be.
You can talk or stealth your way through pretty much the entire game, but no matter how you play you MUST blow up the military base and everyone inside. Also, you MUST kill the one known as "The Master," although it is possible to talk him into committing suicide. So, while you cannot be a total pacifist, it's possible to finish without ever PERSONALLY doing any fighting.

I think end boss fight is mandatory in FO2 as well, beside that there are quests that involve combat and of cource there are the random encounters.

According to PJ's walkthrough you can hack the terminals and talk some people into attacking the end boss in FO2.
No need to personally engage anyone.

To answer his question as best as we can:

"You can beat the games without firing a single shot"
On the same hand though, you can also go through the game and kill. Every. Single. Thing. (Good luck grinding through 3 towns, it gets boring pretty quickly)
This is one of the reasons I'm not a huge fan of Fallout 3, you can't be diplomatic and you can't kill everyone.

I thought it a little sad too that in F3 you could not be completely diplomatic or kill everyone. The killing everyone problem is all because of the ESRB. They didn't want an Adult only rating... I hope they do make a diplomatic way for FNV.