Ashe: If your team lacks a good initiator or the jungler has no hard/soft cc for ganks.
Caitlyn: To outrange your opponent and poke your mirror lane to death.
Corki: When your mirror lane has no escapes, but the support has the ability to peel you off. Use R to secure kill.
Draven: For his strong early game, he becomes irrelevant late game unless you can catch his Q's.
Ezreal: poke, poke, poke, escape, global ult, as buff for team mates. Need I say more?
Graves: I honestly have no idea why people play this champ other than for his ability to take a beating and keep on kicking. Has a pretty good punch too.
Kog Maw: Low attack range, but due to his abilities he has one of the best late games of all of the ADC champions.
Miss Fortune: Great with an AoE team comp and probably one of my favorite carries in the game. She's a lot of fun and her ult range can be a pain in the ass to opposing teams.
Sivir: Spell Shield, Ult. Need i say more? A run speed and AS buff FOR YOUR ENTIRE TEAM? Too easy.
TWITCH: You forgot Twitch. Often overlooked and underestimated. If built/played right he can be DEVASTATING to the enemy team. True. Damage~
Urgot: You add Urgot... and leave Twitch out?! This champ... is not with the meta.
Varus: %HP damage and AP per hit? Seems pretty strong to me, not to mention one of the longest ranged pokes for ADC champs matched with a slow, AS buff, and a immobilization ultimate? Too easy.
Vayne: Vayne is so situational with team comp, lane comp and enemy team comps that its a hard call. She's definitely strong though.