I've been playing for about a year and half now and I usually play support (Taric FTW), because AD carry hasn't really been my strongest role. And from what I can see, each carry is typically situational.
Now I think it's possible to make a subjective tier list for the 14 AD ranged carries in the game. Here are my personal picks, and if you disagree, please let me know what you think it should be.
Also, feel free to submit your own tier list.
1. Ezreal - Great farm, strong throughout the entire game. Free blink and a global ult that can hit the entire team. Even with the nerf to his W, he's still strong in any situation. He does take a bit of skill to play properly, and also his dominance in lane relies on his support and the enemy bot lane comp. His blink is one of my most hated moves in the game due to its ability to move out of CC. If you've ever seen an Ez blinking out of a blitz grab or taric stun, you know what i mean...
2. Tristana - Very strong early and late game, with an iffy mid-game. She gets a free ignite in her explosive shot, and a far-range escape ability that can jump over most walls. Her range is incredible level 18, allowing her to kite and mow down enemies with ease. If you build ArPen on her, she can wipe out tanks quickly. Her ult does a whopping 300 magic damage at level 6, which is a devestating finisher in lane. The displacement from it can also save you or or teammates if done properly. Her Q AS steroid is amazing, and her explosive shot makes farming a breeze.
3. Graves - Strong throughout the entire game, but is reliant on a team who can defend him properly. His innate tankiness is great if paired up with a tanky support like taric or ali. Has a great steroid ability coupled with a useful dash. Most people dont seem to know how to properly use the dash though. Smokescreen is a great slow, and can really screw up an enemy initiation. To me though, his ult feels a tad lackluster, despite being able to hit multiple opponents.
4. Draven - Definitely an underrated carry, as he takes quite a bit of skill with micromanaging his spinning axes. The axes however, provide a huge steroid, and coupled with a great AS and MS steroid, a skilled Draven can make quick work of an enemy team. The bleed from his passive does great DOT, and can usually secure a kill from an unlucky enemy trying to flee. His ult is a strong global snipe that is great for picking off stray enemies or damaging an entire team. I feel like his range is a little low though, so he is easy to target, which makes his late game a little worse than some others.
5. Ashe - Ahh, the old classic. Ashe is a reliable carry who only suffers from having less damaging abilities than other carries. Her passive is awesome for securing first blood, but is really kind of useless late game. Hawkshot provides a free ward every minute, which can save your lane against a gank or be wasted. The passive gold from it is kind of lame though, as it really only provides a free dragon or so. Her volley is a nice AOE poke that is useful for farming and slowing enemies. Ashe is a great kite champion with her frost shot, and a skilled Ashe can really bring the hurt. Her ult is what makes her great though, as it can hit anyone on the map and stun for up to 3.5 seconds if shot from far enough away. While most carries have to wait for their team to initate, her ult can do it from far away and keep her safe to clean up the enemy team.
6. Caitlin - Caitlin isn't as strong as she used to be, due to the wide range of new champions released, but her lane dominance is quite strong. Her traps can be great if placed in proper places, and they can zone the enemy team quite well. Her range is also really nice, and her headshots (while not too reliable) can stack up great damage. Her Q is a nice poke, but it leaves her really vulnerable. Her net is a nice escape or gap closer that can slow too, but the slow is mostly for escaping. Her ult, while doing great damage from afar, is easily blocked and is also not that useful for a team. Many times this ult is used to KS from the team, and it takes a long time to cast.
7. Miss Fortune - MF is definitely a situational champion. She was one of my first champions i bought, and I think she does best against Vayne or Caitlin lanes. Her AS steroid is really nice, and provides the healing debuff effect ignite does. Her passive is nice for kiting from full health and gives her great MS, but sadly even a minion can pop it. Her Q does great poke if aimed properly, and in a teamfight it's like being able to attack twice, but it's situationality makes it not quite so useful. Her E is almost useless damage-wise, but it helps in escaping and slowing the team in preparation for her ult. Her ult is very strong early and mid game, but late game the damage falls off slightly. However, with a strong team with lots of AOE ults like Amumu, Orianna, GP, etc. it can help do lots of damage to the entire team.
8. Vayne - Most people might be surprised that Vayne is this low on the list, but I don't think she's quite as stellar as most people think. Yes, her late game is incredibly deadly, but I feel she is easily countered by champions with more range and high CC. Her damage output is awesome though. Q provides a nice gap closer and escape, and the damage is a nice poke. Her silver bolts take three shots to do true damage, but the true damage dealt is what makes her so strong. In lane, the silver bolts aren't the best unless the enemies are locked down, as it is easy to run away and let them expire. Although this can effectively zone the enemy team. Condemn is a nice way to get an enemy off your back, but it's hard to pin them to the wall if the team is smart. In teamfights, condemn is even harder to pull off, especially when assaulting the enemy base. I personally don't like her ult that much, but it does provide a lot of AD and MS. The stealth tumble has to be very clutch, and if it's not properly executed, it could mean the end for Vayne.
9. Corki - Corki is definitely a great powerhouse, doing a lot of nice sustained damage that increases over time with his E. He has a good escape and initiate with his W, and his Q is nice for revealing enemies with minor AOE damage. His ult has nice range and is a good poke ability and can be spammed often. His passive does true damage with every AA, which is nice against tanks. The problem with Corki though is that all of his abilities except for his gatling gun do weak magic damage, and his gatling gun has to be in melee range to use. Building AP on him is useless as he has horrible AP scaling. He seems very outclassed to me, and doesn't synergize well with many supports except for Taric.
10. Varus - Varus has a really nice poke with his Q, but it can be hard to hit, and minions block quite a bit of damage from it. His blighted quiver does pay off with its damage, but it is kind of clunky and hard to pull off. His hail of arrows does pretty low damage despite scaling with AD, and it's slow leaves much to be desired. He has a really hard time kiting people. His ult has pretty good range and can hit multiple people. It provides a nice snare, but it is very slow and hard to hit with. Enemies can still attack while it is active, so it's not all that useful if it targets the wrong person. Also, his AS steroid from his passive isn't really that great, and it's hard to pull off. The time it's active is shorter than the time it takes to get into position to attack an enemy. His movement speed and health are also very low, making him a very easy target. Something about him tells me he's not meant to be played as a straight AD carry, but hybrid builds don't seem to work well on him.
11. Kog'Maw - Kog is definitely a late game champion. his Q gives nice passive AS and a low damage active that gives a nice defensive debuff. It's very low range though, and moving into position can really set you up to be focused. W gives a really nice range buff and does good health damage percentage, but when it's on CD, it leaves you vulnerable. E is an OK slow that does a little bit of damage, but it is easy to walk around. His Ult does nice damage from afar, and a great Kog'Maw player can really make the enemy team's life hell, but it uses up mana really fast, and building mana on AD kog'maw isn't very beneficial. His passive is ok for getting kills after you've died, but if you don't kill anyone, it really doesn't help at all. Fast champions can simply run away from it too. AP Kog'Maw does a lot of damage with his abilities, but I'm talking in terms of straight AD (on-hit Kog doesn't count either).
12. Sivir - Sivir is a good kiting champion with strong damage on her Q. Her spell shield is nice to get mana back (sivir uses a lot of mana), and a smart sivir can use it well every time, but a bad Sivir will only make herself OoM by doing it. Ricochet does OK damage and it's strong if you level it up first, but you'll do more damage leveling up Q. It's not very effective for farming early-game either. Her Ult is a nice AS and MS buff for her and her team, but it's not all that useful in my opinion. Yeah, it's like a free Shureliya's, but it requires a strong team to make good use out of it, also, not everyone on your team is going to be doing AAs either, so they kind of get it for no reason. Her passive is nice for chasing and kiting, but a slowing ability will make it useless.
13. Twitch - Oh how the mighty have fallen. Twitch is definitely capable of doing great damage, like any of these AD carries, but his usefulness his very low, and he's very easily countered. Anyone can counter him actually, for just 400 gold with oracles. The stealth on twitch is nice, but it takes a long time to activate and it only lasts 8 seconds at max level. The new MS buff on it is nice, and it does give good AS bonus, but when Twitch revels himself, he will easily be the first person targeted. The true damage from his passive his nice, but it requires sustained AAs on his target. Twitch's squishiness will surely cause him to fall faster than he can get full poison. Expunge does a lot of damage, but it's effectiveness requires twitch to get full stacks of poison on his target, which can be hard to do if he is targeted first in a fight. His new venom cask is really pretty lame, despite giving stacks of posion on the enemy and an AOE slow. I feel like it should at least do a little bit of damage when activated. His ult has changed from before, and while it doesn't have an ammo limit, it now does much less damage. The AD steroid from it isn't very strong, and despite piercing through enemies, the pierce effect gets weaker with each subsequent enemy hit. Also, his Ult is very hard to hit with, and actually makes him more of a target. Twitch relies on a very strong team, and he really only provides damage for his team without doing much else for them.
Whew, ok. So these are my personal opinions, please let me know what you think. If you are giving feedback, make sure it is thought-out and intelligent. I'd like to know what the rest of the community thinks.
EDIT: Decided to remove Urgot as he doesn't really fit the role as a ranged ADC.