Not everyone plays the game as a packrat, but sometimes you come across an item you just can't bear to give up. For me, it was probably Lil Timmy's Peashooter-- I came across it early on in Deadmines with my warrior, and used it to pull all the way up to level 60. Of course, on my first raid, our MT checked me out, and the next day I had a gun in my mailbox with some Stamina and Strength on it. I thanked him and equipped the new gun, but felt a little pang of sorrow saying goodbye to my Peashooter-- in fact, it's still sitting in the bank.
There are some good ones in the thread, too-- Severed Night Elf Heads (from a previous iteration of AV), holiday items (I don't think my warrior has ever actually used that food horn, but I always have it with me just in case), early epics and set pieces, and quest leftovers. My shaman still has a charge or two left on his Mechanical Yeti-- I keep saving it thinking that someday we'll be in a raid fighting Raggy or Nef, we'll start to wipe, and my summoning the yeti will be the final straw we need to take the guy down. So what do you have taking up valuable inventory space that you can't bear to part with?