Infocom's Enchanter text-adventure might have the quickest-to-unwinnable-state of them all. The first command of the game can be FROTZ ME, magicking the player character into a light source. The thing is, FROTZ can't be turned off, which makes it impossible to find the correct portrait in the picture gallery.
In practice, there's the ridiculously helpful bug that "EXTINGUISH ME" worksnote Essentially making the intended "can't unFROTZ something" effect completely nonexistent. Brilliant programming, there.. FROTZ originally used the same code as the command to LIGHT or EXTINGUISH a normal light source like a lamp or a torch. It wasn't originally intended that you could "turn off" a glowing object (such as yourself) that had a magical light spell cast on it. When Infocom corrected this "error" in a later version, a common player trick for making sure you were never deprived of a light source suddenly became instant unwinnability. Infocom eventually decided it was better off changing it back, even though the text you get from EXTINGUISH SELF is rather nonsensical.
You see this problem crop up in later games. Sorceror, the sequel, makes it a firm rule that FROTZed objects can never be EXTINGUISHed, always allowing you to make the game unwinnable (by Design) on the first move. The final game in the trilogy, Spellbreaker, goes 180 degrees on this and explicitly allows you to EXTINGUISH FROTZed objects (with the message "You dismiss the magical glow, and it fades"). But in that game, there's hardly any point in doing so, short of turning yourself into a grue.
Infocom's only console game, the NES adventure game Tombs & Treasure, succeeded in playing like its PC cousins too well. There are places where combining items in the wrong order, or forgetting an item, makes the game unwinnable.
Not so much combining items in the wrong order than combining them at the wrong time. At one point, you find a magnetized rod and a shallow bowl. You put them together to form a compass to navigate a maze. Pretty smart, right? Well, don't do it right away, or else you won't be able to use that rod to remove a small iron key from inside a hole too small for your fingers.
A patch release for Return To Zork fixed some of the harder puzzles in the game but could cause one of your inventory items to vanish suddenly. Unfortunately one of the last puzzles in the game requires you to throw all your inventory items into a pit to raise the bridge. If that last item happened to get snatched by the glitch you were left staring at a bridge just one step short of allowing you safe passage across the gap.