I browsed over the first posts and I'm surprised to not see any mention to Dr. Jekyll's cane (game: Dr. Jekyll and Mr. Hyde - NES), which doesn't do anything, or if it does, it needs to be almost pixel perfect to hit anything. Maybe it's so bad it can't be considered a weapon...
I hate Megaman 3's weapon "Top Spin", but even more that freakin' MM5 "Charge Kick"! The "Super Arm" from MM1 is useless without the special rocks nearby, and they are rare.
I'm also not fond of Halo Series's Plasma Pistols, though I wouldn't call them useless.
Oh! I remember a good one! The Dagger from Super Castlevania 4! I absolutely love the game, but that weapon is really USELESS! It's weak (I believe even weaker than your normal weapon, the whip), and the only thing it has going for itself is that it flies straight in front of you (aka, range), but the whip can get so big that anything that is in front of you might as well be whiped instead of stabbed!