This requires you to play through the entirety of Half-Life 2: Episode 1 firing only a single bullet. (Right after you find a gun, you're required to use it to shoot open a lock.) This actually turns out to be easier than you'd think; a big reason is that, according to the developers' commentary, Valve originally planned to keep the player gun-free much longer than they actually ended up doing, and so many of the combat scenarios later in the game are designed so you can beat them in alternative ways. Doing this ends up turning HL2:Ep1 into a bit of an adventure game, or at least making it more tactical: you're always on the lookout for, not just explosives, but other useful items such as hopper mines, radiators, and cinderblocks that can be used to defeat the enemy.
I love this one. You have to pick up a garden gnome hidden under a table at the very beginning of the game, and carry it with you the whole way -- through caves and mines, Combine ambushes, and wild high-speed car chases -- to the rebel base at the end so you can load it into their rocket and launch it into space. It would be nice to think that the gnome is a nod to Psi-Ops, a game I worked on a little while back which happened to be infested with gnomes, but eh, it's probably Amèlie instead, right?