Give details - why is the game system a good fit? What matches the Fallout setting?
GURPS RPGGEEK is almost always a great answer. I would suggest it if you want a 'crunchy' Fallout experience. You asked for specifics, so here they are:
In Fallout, you can encounter futuristic robots, WWII firearms, 1980's computer systems, barbarian villages where the pinnacle of technology is the plow, and nomads who's crowning achievement is the pointy stick. GURPS has always had support for multiple Tech Levels. It'll support PCs from any of those tech levels interacting with equipment from any of those tech levels.
As mentioned above, Fallout was designed for GURPS originally, so it's got a lot of meaningful weapon variety. In GURPS, there are many different variables in weapons, so you can have two semi-automatic pistols without them being the same except for their descriptions.
Aside from weapons, GURPS has good rules for computers, armor, vehicles, medicine, and pretty much everything else.
GURPS allows you a lot of freedom to create mutants, a big part of the Fallout appeal. Designing new races is pretty straightforward, so you could have templates to make all those things you encounter in Fallout recognizable, but not all the same. Ghouls (Is that what those irradiated guys are called? Can't remember.), giant animals, supermutants, vampires, murkloks (?), etc..
For a GURPS Fallout campaign, I'd recommend the following books in addition to the core:
There is a Fallout PnP system that uses the exact system in the computer games. Which, luckily you can find in No Mutants Allowed.
Whenever I play Fallout in tabletop environment, I use those rules. It is much more Fallout-ishy than anything else
Fallout the computer game was originally designed using Steve Jackson's GURPS - and an early name was "Vault 13: A GURPS Post-Nuclear Adventure"! Sadly the corporate relationship fell apart, but as you might imagine it is still similar to it in feel and execution. There is a pretty good GURPS fan conversion for GURPS Fallout as a result.
Darwin's World is a d20 Modern game inspired heavily by Fallout. There is a Savage Worlds version of Darwin's World too if you want different mechanics.
Exodus: Post Apocalyptic Roleplaying was originally specifically called "d20 Fallout" before some kind of problem with the licensing.
So if you have a soft spot for GURPS or d20, both are good fits - explicit conversions, large player base, and many other supplements and sources to draw from.
As much as I hate seeing people answer their own question, here's some results from my own research, in case others stumble on this topic...
Deadlands : Hell on Earth - A good, quick system. Rewards player participation, and self-moderation of disadvantages. Supports differing levels of technology, but no concrete rules for a lot of high-tech items, like computers. Some setting-specific rules and character types, but easily adapted.
Twilight:2000 - No support for mutants, but lots of realistic millitary rules, and radiation effects. The first edition was pretty bad, but the second edition was a fairly simplistic system, using d20s. Good support for modern skill sets, but the character generation rules might suffer a little in a true Fallout setting.
Aftermath - a really old-school post-apoc game. The basic set had details of many different apocalypses.
d20 Modern/Future/Post-Apoc - It's d20 3.5. What else needs to be said? Nothing specifically supporting Fallout, but reasonably good generic rules, if you like class-based systems. Can be good for introducing players familliar with d20 mechanics.
Gamma World - A little too fantasy-oriented for Fallout. The high-tech gadgets and mutants are of a different style to Fallout, but at least there is plenty of variety. The latest version is even less crunchy than the previous ones, and would suit Fallout even less.
Honestly surprised this wasn't an answer here already but here's why I think it fits:
- The setting is post-apocalyptic by default but doesn't assume a specific cause of said apocalypse, so tailoring it to accurately reflect the fallout universe is a piece of cake.
- The PC Classes are designed to evoke the various clichés and archetypes that the post-apocalyptic setting is defined by.
- Light and Fiction-driven rules mean that your players are free to explore the wasteland as they see fit and the MC (AW's Game Master) has all the tools they need to make it happen with little to no prior planning.
- Combat is gritty, dangerous and can be resolved on a variety of scales (from a one-on-one shootout to a full-on faction war) with simple mechanics.
Possible Hiccups that may have to be accounted for:
- The Psychic Maelstrom is a core part of Apocalypse World (as are the playbooks that rely on it) but I don't think it has a direct analogue in the Fallout universe. On the other hand, I don't feel like it would clash over much with it.
My Experience: Fallout in all but name
While I unfortunately have no experience with playing Apocalypse World to follow the canon Fallout setting, almost all of the Apocalypse World games I've participated in have been rife with mutants, bizarre technology (both 'ancient' and homegrown) and freakish monsters all wrapped up in a dusty post-nuclear wasteland of gangs and cobbled-together settlements in the ruins of civilization.
The only missing thing in my own experiences is that my players were all happy to embrace the Psychic Maelstrom and the weirdery therein. As mentioned above this might clash a little with the Fallout setting. I don't feel like its inclusion would detract from the Fallout 'feel' but it's definitely an addition that doesn't have any precedence in my experience with the setting.
We've played Exodus for a couple of sessions so far and we are really enjoying it. It's Fallout with the serial numbers filed off. (Apparently, they didn't do a very good job on that, due to the lawsuits involving the game.)
Exodus uses the d20 system with a ton of new material that sticks very closely to the source material. Chances are, if you chose a Perk in one of the games, it's now either Trait, Feat, or Talent. Character creation is pretty free-form. You select a Background and Profession, which give you access to class skills and bonus feats. (You also 'tag' three skills, which always gives you access to them and you can advance them above the normal rank cap.) Then you choose either the Offensive or Defensive class.
Don't forget the freely available Mutant Future from Goblinoid Games, a retro-clone of Gamma World.
The game supports both old style weaponry as well as mutant humans. Your GM can leave out the spidergoats if he wants.