I never use mines, the Fat Man, the Missle Launcher, Flamer, 'Ol Painless, Plasma Pistol, Sawn Off Shotgun, 10mm Submachine Gun, or the Double Barreled Shotty.
I crossed out the ones I do use, but don't use the others. Also Lincoln's Repeater, T51-b power armor, pre-war clothing, including hats, baseball cap and all headwear (except Lucky Shades and headwrap), vault suit, armored vault suit, radiation suit, 10mm pistol, hunting rifle, BB gun, combat shotgun, switchblade, Firelance, Alien Blaster, Laser Pistol, Laser Rifle, pulse mine, pool cue, sledgehammer, super sledge, shovel, auto axe, ripper, chinese sword, power fist, Clover, Jericho, Dogmeat, Bloody Mess perk, Here & Now perk, Nerd Rage perk (and a bunch of others), Nuka Cola Machine - it just never works for me. It swallows my Nuka Colas and remains empty, and as it takes up too much room I just don't bother with it.
I think that's it. It's all I can think of, anyway. I've tried them once, maybe, but decided I didn't like them/they didn't suit my characters. In the case of some of the weapons they just sound bad (ripper, power fist, combat shotgun)
The unique weapons and armor I just toss in a locker in my house. I can't sell them, must collect the different things even if I never use them.
Just to be different I should make a character that only uses those things. But, I'm sure he/she will suffer from the problem a few of my characters have had - can't get past level 4 because I get bored with them.
Edit: Missed a few after reading previous posts.