I'm going to start by saying that Gamma World IS loads of fun in play - I highly recommend the game. I'm unsure how it will play in a long-term campaign (it's too new to have an opinion on this) but it can work very well both as a short-term campaign (say, the time frame of your typical Cthulhu campaign - GW, like CoC, is a high lethality setting!) and for one-shot games. It's this latter aspect of the game that I really like; it can serve as a great "party game" because the MECHANICS make it just as fun as the SETTING does.
Physically, Gamma World is a fully self-contained boxed set, containing a comprehensive 160 page digest-size rulebook (containing all pertinent 4E rules, so it is NOT necessary to have, say, and D&D books), two packs of cards - Alpha Mutations and Omega Techs, a card booster pack, various maps, and a couple of sets of thick cardstock punch-out chits representing iconic GW monsters (adding to the old-school feel of the game). The book is made of nice stock, and the four-color artwork is evocative and amusing.
Gamma World, of course, is based on WoTC's 4E ruleset; GW uses a pared down version of the rules (akin to the D&D Essentials line) - involving throwing of dice - and adds to that elements of a card-based game. It works very well for Gamma World because the cards introduce randomness (random generation of mutations and strange techonology) and because it's the nature of GW mutations that they have a non-sequitur quality to them.
The first part of a Gamma World game - and practically a mini-game in itself - is character generation; my group, preparing to run the game for a DDXP weekend, spent about an hour generating characters; this is done with the group and GM at the table. Players roll 2 d20s, referencing the rolls against two Origins, one primary and one secondary - choices include such things as "Android", "Gravity Controller" and "Yeti" - and it is from these that one derives the primary and secondary ability scores (for example, my Android Gravity Controller had an 18 Intelligence and 16 Constitution), as well as At-Will powers (keyed to the stat linked to the Origin), skill bonuses, defense bonuses and so on - the Origins are essentially the character's "class". All other ability scores are rolled - yes ROLLED with 3d6 - again keeping with the random craziness that is GW.
Armor and weapons are described not in specifics, but in generalities, such as "Light Melee" (keyed to Int/Dex), "Heavy Armor" (AC 7, -1 move) because it's up to the player what these are - for example, you might decide your "Light Melee" weapon is a skillet, "Light Ranged" is a bag of billiard balls, and "Heavy Armor" is a collection of trash can lids duct-taped together - the description can be as serious or silly as the player likes. Again, GW uses a mechanics-lite version of 4E.
Once the Origins, stats and equipment are decided upon, it's time for mutant powers! Every player is dealt one card from the Alpha deck (mutations) and the Omega deck (ancient tech); Alpha powers themselves have origins (if these match your Origin - for example "bio" or "dark energy", you can overcharge them at a risk of greater effect - more gambling!) and vary in power type (most are Encounter, it seems); the Omega techs run the gamut from a fusion rifle to an animatronic toy which immobilizes opponents. Players can build their own card decks to use (and there are rules for keeping this fair, as well as situations in which they must draw from the GM's deck) as well.
Once character generation is complete - and players have a chance to describe their hapless warrior of the wastes - the game follows the familiar 4E encounter structure (with short and extended rests). There are simplifications - no one has surges, for example, just one second wind per encounter (yes, GW is high-lethality) and there are no action points. More random craziness ensues - after each extended rest, all players turn in their Alpha card and draw a new one (as reality changes in a process called Alpha Flux); if any Omega card has been used, a d20 roll is made for the tech to see if it broke (1-9 it broke, 10-20 it's reusable) - broken techs sometimes have salvage rules on the card, so all isn't (necessarily) lost. After a typical encounter, players will draw an Omega tech card to add to their pile (treasure!) As for hazards, they can be wacky (savage bunny men called Hoops) to deadly (the lethal Eviscerator warbot), and natural hazards - like radiation pools - can add or subtract new Alpha powers along with the damage. Anything goes!
The setting's backstory is an update from the traditional "nuclear war" - there was a little problem with the Large Hadron Collider (the "Big Mistake") which has caused the worldliness of multiple universes (think Hugh Everett's "many worlds hypothesis" here) to get tangled up with each other, so that multiple realities are being expresses simultaneously: this is the cause of Alpha Flux, which can change characters from encounter to encounter (new Alpha cards) and certainly keeps the game amusing as one has a "core" character with alterable mutant powers!
From a GM's perspective, as I mentioned before, I don't think the game would support a long-term campaign (or a "serious" post-apocalyptic game), but it's perfect for a short-term campaign (characters are capped at 10th level, anyway) and GREAT for a one-shot at a party or as a break from another campaign (my group may play it as a break from our long-term Traveller campaign, for example) - that's its real strength, for me: it satisfies that need for something more "RPGish" than a board game, but less commitment-intensive than a proper "campaign". It's also a good template for wackiness and humor - just a fun game to play.
