Assassins, Vanguards and Enchanters are those I feel need a Roster Update the most.
Assassins often create very frustrating counterplay experiences, though a lot of them do have very fragile weaknesses, they need some more ease for enemies to utilise them. Also, their itemisation choices are really lacking, since almost all AD Assassins build the same as Marksmen (after they finish Youmuu's and Duskblade).
Stealth is also a weird mechanic, that could definitely have potential (maybe all enemies would see a danger sign, when a stealthed champion was close, except in brushes, where they would always be completely invisible).
Vanguards are generally lacking in itemisation clarity and diversity, and none of them fulfill any kind of strategi reason to be picked (other than "I have an AoE-combo where I smash into the enemy team with CC").
Maybe also more interesting thematic components (maybe Malphite would have a passive with a CD to cause earthquakes around him when he used an ability - then of course his abilities wouldn't be AoE in their isolated states).
Enchanters don't need a lot of messing around with, since (if you ask me), they're actually very balanced. The only thing would be a little more strategic diversity (reasons to pick, let's say, Nami over Sona or Sona over Nami). Also, Nami shouldn't be able to purchase boots :P