I wouldn't mind doing one at all because I really like the game and how goofy you can run it, or with some tweaks its more of an X Men type game. Or Rifts. Or Fallout. (And for a Fallout game, tell me this isn't THE BEST MUSIC EVER for its late 50-early 60's feel: )
While my actually running the game and what silliness level I would do depends on the potential players and what they want, the following house rules are ones I would probably use no matter what:
1: Origin Rolling: In Gamma World you normally roll for two origins, with a double roll (made nearly impossible with the expansions that add in even more origins) on the chart equaling Enhanced Human as one of them. For my house rules, players may choose one or both origins at a starting XP penalty of 125 each, or 250 for Enhanced Human and you MUST roll for the second origin. Players selecting one of their two origins must choose it FIRST then roll for the second one.
2: Ability Scores: In Gamma World your first origin is your primary and the second is the secondary. (NO WAY!) Your origins give you an 18 in its' ability, and the secondary a 16. Normally you roll 3d6 in order for the other 4 abilities. BEFORE ROLLING, players may choose to assign the 4 rolls as desired, and instead of 3d6 roll 1d8 and add 8. (Meaning instead of a spread of 3-18 you have a spread of 9-16 and choose what to put where.)
3: Alpha Mutations: Normally you draw a single card and deal with it. But normally your Alpha Mutation changes every time there is an Alpha Flux or an Extended Rest. This is a little too random for me so here is what we will do: At creation the player draws THREE cards from the deck and chooses ONE. Outside of an Alpha Flux or other in game effect that would cause a Mutation change this is your PC's power. When something comes up that would make you draw (Extended Rest changing being removed.), you can instead burn a Healing Surge and keep your power. Draw 3 select 1 also happens for your level 4 and 8 choices. There is NO power draws outside of Flux type events or character generation.
4: Player Mutation and Tech Decks: These are BANNED unless the player chooses at creation to instead of building a 7 card deck, build an 8 card. The DM at start gets to draw and KEEP a card. If you are going to be a degenerate munchkin paying 4 dollars for a package of 8 blind buy cards you must pay the DM for this right. By giving the DM one of them. Tip your friendly neighborhood Dungeon Master. (At DM's discretion other gifts such as booze, candy, toys, or helping them clean up after the game could be accepted as well.)
5: Keeping your Omega Tech even when you shouldn't: Normally an Omega Tech item either degrades or goes Tubby Bye Bye when used. If you REALLY like your new toy you may choose to keep it upon receiving it (aka you make the choice THEN AND THERE, no waiting) you PERMANENTLY sacrifice 1d3 Healing Surges and its yours for the life of the PC. If for some reason you have no Surges left to sacrifice after the roll, (Like your PC has 2 Surges total and you roll a 3 meaning you now have -1 Surges) your PC is now unable to use ANY Omega Tech cards at all. This also means you LOSE all Omega Tech you previously owned instantly. It serves you right for being that greedy with your toys. Outside of permanently sacrificing Healing Surges to keep an Omega Tech card, failing an Omega Charge roll works as normal.
6: Gun ammo: Normally in Gamma World you get ONE shot with any gun or ammo type weapon, and if you use it a second time in an encounter its out of ammo permanently till your PC can somehow find more. This is sort of silly. Instead of a heavy accounting of ammo now you have the PC's level in shots per encounter PERIOD. No overshooting. Whenever the PCs go to any place capable of salvage or to purchase more ammo the DM will tell you how much it will cost (or time wasted, probably spent in Healing Surges for the day) to stock back up on ammo. Whenever a 1 is rolled to hit with an ammo weapon it has run out of ammo for the encounter, AND until the character can find some reloads.
7: BE A MAN: Roll for everything by the book and accept whatever you draw for your Alpha mutation and start with 250 bonus XP. If you choose this bonus you may not expend surges to keep an Alpha, but may sacrifice 1d3 to keep an Omega Tech. You may also never use a player deck of either, and never get to draw 3 take 1 at level 4 and 8 either.
8: D&D Essentials Races for an Origin: These may be chosen and counted as Enhanced Human either in rolling or taking a 250 XP starting penalty for creation. Any abilities of the D&D race that are not applicable to Gamma World are ignored but otherwise the race works as listed.
The above I think makes for a slightly less ridiculously random game with a more stable Gamma World Earth as opposed to one where everything and everyone seems to change what they can do constantly.