Corki - I've laned with a Corki who spamed his joke and taunt commands once. I've learned to hate his voice.
Darius - I've only seen a free Darius week once. During that week he was instalocked by one of my teammates in every single game.
Draven - Never seen him free.
Fizz - Never seen him free.
Gragas - Just haven't gotten the opportunity yet. I plan to play him at some point before the rotation changes though, since he's free right now.
Heimerdinger - Never seen him free.
Kassadin - Same as Gragas.
Kha'Zix - Same as Darius, with the additional fact that Kha'Zix has only had a single free week since being released.
Lee Sin - Never seen him free.
Malzahar - Never seen him free, have not yet bribed my friend, who mains him, into letting me try him for a game or two on her account.
Rumble - Never seen him free.
Shaco - Never seen him free.
Shen - Never seen him free.
Trundle - Never seen him free.
Veigar - Never seen him free.
Viktor - Forgot to try him the one time I saw him free. Otherwise, same as Malzahar
Xin Zhao - He looked boring, so I never bothered to select him during the one week where I've seen him free.
(I would try to convince the poster above to play Poppy as we're supposed to, but honestly I hate Poppy as well. Whoever gets me should probably focus on either Corki or Xin Zhao, since all the other ones I've listed, I do want to try, I've just never gotten the chance to do so.)