This is a cool thread, lots of interesting ideas!
Here are a few of those I've done in the past.
Half-life - Crowbar only.
Similarly for HL2 and the episodes crowbar only except where you are absolutely required to use another weapon.
Sounds intriguing. I rarely used ammo on headcrabs, zombies, or vortigaunts. Marines are tricky but usually can be lured around a corner. The rather open outdoor areas sound ridiculous though, also certain parts of On A Rail. I imagine Xen consists of a lot of running and dodging thanks to the overlords.
But I DO know that the crowbar can deal the final blow against Nihilanth, heh. You kinda glitch through his body which is trippy. Pretty sure the crystals have to be destroyed though, which probably requires a gun.
An interesting "challenge" was the excellent Counter-Life mod. The Half Life 1 campaign, except with Counterstrike weapons. Enemies grant money on death, all map pickups are cash bundles. You have to buy everything from health terminals. It has the kill-fast-die-fast vibe of Counterstrike, particularly against marines. Forces tactical play and cover (or excessive sniper rifle use, of course). I loved getting knife-kills on marines, IE ambushing them.
http://www.moddb.com/mods/counter-lifeI don't understand how HL2 can be completed with just the crowbar though. In particular there's that one part where you have to defend a terminal during the revolt while Alyx hacks it. There were just so many enemies, and I'm pretty sure they destroy the objective if you aren't fast. I should look up that gravity gun LP someone did...
Deus Ex - Non lethal completion, prod and tranq-dart takedowns only. Managed to get a fair way through a no weapons/items run at one point(reached versa-life) but lost the save during a computer migration.
I think I managed this, mostly used the stun baton rather than the prod (and all the tranq darts I could get). It took a long time and lots of reloading, mostly due to the MJ12 troopers. They have this small baton-vulnerable area on their lower backs, it's weird and not marked.
Pretty sure it's possible to complete the game with absolutely no kills, though I don't remember how you avoid killing Navarra. May be a glitch. Gunther you can just run past which I find hilarious, that game sure was open-ended in many ways.
It-He loves to break games. He knocked the terrorist leader unconscious then carried him through several levels. He also managed to wipe out the entire hotel ambush through pre-placed LAMs and explosive crates. I highly recommend his screenshot wrong-plays of Deus Ex, Thief, System Shock 1, and every Ultima
http://www.it-he.org/deus.htmSkyrim - No merchant run. Only able to use what you can loot/steal. This includes spell-books, you have to find them as loot. Variants of this in the other Elder Scrolls and Fallout 3/NV games, but Skyrim is the only one I've actually completed the main quest and a good portion of the side-quests/major storylines.
This sounds like such a relief, and not that hard. The only things I buy are crafting materials anyway. And leveling smithing past like 40 is a waste, since you can max armor protection with fortify smithing potions and leather. As for spell tomes, magic is kinda weak compared to the almighty stealth archer.
Fallout - New Vegas - Varmint rifle only. That rifle you are given for target practice at the beginning of the game? Your only weapon you are permitted to fire. Can carry other weapons to repair with but not for use. Have fun with deathclaws.
Is the varmint rifle even good enough to hurt a deathclaw *at all*? I really resent the damage threshold system. I guess this challenge would involve avoiding deathclaws and running from everything else.
Fallout 3 - Similarly to the above, the BB gun you get during the intro is your only permitted weapon. Spend a lot of time running between merchants trying to find ammo. Excludes points where you lose access to your equipment such as during operation Anchorage.
But... Even if you beeline the main quest you'll be facing enemies with power armor. Do you just run past? And going on sidequests or clearing vaults is just ridiculous, there's so little BB gun ammo and the damage is pitiful.
X-Com - no plasma weapons/alien weapons, no armour above personal, no psionics. Actually managed to complete this one after many attempts with the alien brain shot down with a pistol.
X-Com - Hawaii single base run. Managed to get surprisingly far with this, up to my second alien base assault before it collapsed.
If this allows laser weapons, not all that hard. But I suspect you mean no laser weapons. Interesting challenge, congrats on the execution.
That single base run sounds hard or impossible, yeah.
Bloodbowl - Orc, all lineman team. Managed to make it through to win the cup, but so many deaths of rookie linemen. Attempted this with a halfling team once. Much squishing.
Haven't tried this game yet, sounds fun though.
A challenge I've thought about a few times but never did was the X-Com: Apocalypse Renegade Challenge. See, in Apocalpyse if you fuck up the Government enough that they go hostile to you, you stop getting monthly payments but the game actually keeps going. The way to survive would be by the old staple of X-Com: churning out advanced weaponry and selling to the black market. An even harder version would be to make as many factions hostile to X-Com as possible.
This doesn't seem so bad (even though this game introduces diminishing price on things you sell a lot) but I only got to the introduction of energy shields before I had to put my playthrough on hold. Most of my money was definitely coming from manufacturing and selling equipment though. And I don't think the government has anything to harass your craft with (unlike Megapol or the gangs).
Hotline Miami
Milo the Drill: You can only kill enemies with the drill. Believe it or not, I got through most of the game in this run. Granted, I didn't do Assault or Chapter Five because A. that is insane and B. I got A+ on those levels anyway and that was the main point of the run. Still intense.
The worst thing about that drill is the high-pitched grinding sound it makes. Even in such an ultra-violent game those executions felt sick somehow. Also its tiny swing that - wait, does it work on dogs at all? I couldn't get it to. It's a pretty helpful weapon for getting A+ though, since it's not much worse than punching and it gives a ton of score (though I think that was nerfed in a patch? I don't have the Steam version).