I would say the M-16A1 or AR-15A1 when using 62 grain surplus ammo. These rifles have a 1/12" twist barrel, which was designed for the earlier 55 grain round. It is not a fast enough twist to stabilize the longer 62 grain rounds. The bullets quickly destabilize (i.e., go a$$ over elbows right out of the barrel) and produce inordinately large groups with keyholes.
Now I realize that any rifle will have horrible accuracy if it is used with ammo that is improper for its twist rate... I only mention this one because our military actually fielded this rifle and this round at the same time... they advised that 62 grain ammo was for "emergency close range use only" in A1 rifles.
For a rifle to be incapable of hitting man-sized targets at 100-150m, it would have to shoot worse than 20-13 MOA, respectively. There are not many rifles in existence that cannot shoot better than that when used with the ammo they were intended for... even the earliest 18th Century rifles could do a lot better than that. That is worse than what most smoothbore muskets are capable of! There may be rifles here and there that were so screwed up by the factory that they shoot that inaccurately though.
For instance, the most inaccurate rifle I ever owned was a DPMS AR-15 with a 16" barrel. It shot 10" groups at 50 yards. That would come out to right at 20 MOA, which means it would barely do minute of man at 100 yards, and would do worse than minute of man at 150. I honestly have no idea what made it so inaccurate. I solved the problem by selling the upper cheap and buying another one.
Of course, any rifle can produce horrible accuracy if it has a pitted or worn out barrel. I have an M1917 that is a .30-06 shotgun. I bought it for $110 at a gun show. The bullet comes apart as soon as it leaves the barrel, and peppers the target with jacket fragments at close range. It has a nice copper-colored muzzle blast. Suffice to say I quit shooting it after I noticed this phenomenon!
