When I play AP Ez, I use magic pen runes, sorcs and a void staff. I can one shot targets that don't build tanky and have mr up to about 75, because with my pen 75 mr = 18 mr.
In a recent game 18 lvl Varus with a typical AD Carry build + a Mercurial Scimitar that gives +45 mr, died to my E+W+Q from full health.

AP Ezreal has the fastest cooldown in the league to which only Ryze can really stand up:

Q - has a cd of 2.4 sec, 1.4 if you land that Q.
W - a cooldown of 5.4 sec, -1 sec for every Q you land, if you are good about 3.4 sec.
E - a cooldown of 6.6 sec, -1 sec for every Q you land, if you are good about 4.6 sec.
R - a cooldown of 48 sec, -1 sec for every Q you land, if you are in a constant fight and are good, about 25 sec.

Ezreal is a spell machine gun.
If you don't have 40% CDR, you are not being serious, because Ezreal benefits from it in Square with his Q.

The problem with AP Ez is that he brings nothing to a team other than damage since the Essence Flux nerf. While the same could be said for AD Ez, AD has more sustained damage and actual sustain with lifesteal and functions extremely well as an AD carry (AP Ez does not sustain well even with loads of spell vamp, and actually probably sustains better with lifesteal but won't have any). AD also does not rely on skillshots for DPS.

Ez is a strong champ on this map, but shines when built AD.

I do build hextech gunblade late game for sustain, which lifesteals of my Q lichbane ap damage and spellvamps off my W/E/R, it's enough sustain really.

Yes, you are totally right, AP Ezreal brings nothing to the team other than tons of damage.
Other than that AP Ezreal's actual damage output is far greater than AD Ezreal, greater than ANY ADC for that matter. More burst damage and more sustained damage, any damage.

That's how I build him atleast - glass cannon with extreme mobility.
The only cons is, you die in a split second if you make a mistake, because you are squishie like that.

You have only one valid point - AP Ezreal relies on skillshots, and that is correct. You can die, or not get a kill just because you missed a Q. Decent skill makes AP Ezreal shine.

I don't think that either AP Ez or AD Ez is the be-all-end-all for Ezreal play in ARAM. It is entirely dependent on the team he's on and his opponents. If the team is already full of mages who don't really have any other option, I'd slap my teammate silly if he chose to go AP as well. At the same time, on a team full of AD champs, Ez certainly should go AP to give the team some high magic damage. But in cases where it isn't that clear, it'll depend a lot on the other team. If the other team is full of squishy targets, AP Ez would make a lot of sense, as he'd be able to poke them down easily and can combo a single one down pretty fast. But if the other team has several champs that are going to be pretty thick targets, AD tends to work better against those. I also feel like AD Ez probably kites a bit better if they do try to get into his face to pull him out of a fight. So it really, really, depends on what your team needs and what will be best against your opponents.

But let's bring the Ez discussion somewhat back into the realm of the tier list itself.

On the list of poke champs, Ez could possibly be considered a 'mage with 2-3 nukes' if played AP. As an AD he does lose a little bit of poke damage, but at the same time, he's still got a ranged auto-attack which itself can be solid poke. But in the list for actual mages, I'd probably place AP Ez as a wildcard, since his main damage will then truly rely on landing skillshots. But I do think that AP Ez can function viably enough as a mage that he should probably be put onto the mage list somewhere.

I'm back! Thanks for the feedback so far. In this update, I've done the following:

Leona moved down to Tier 2 tank (from T1)
Rammus commentary added
Warwick moved up to Tier 2 tank (from T3), commentary added
Kayle added to Tier 3 poke, and now has her own section with the supports and hyper carries

Still not moving Sejuani - I'd rather have any champion above her tanking for my team at this point, looking forward to any Sej changes that Riot makes though.

If it was my tier list, I'd swap Rammus from T2 with Hecarim from T3. I just feel like Hecarim offers so much more to a team. Between sustain, long ranged initiation, good damage and decent control, he just seems to contribute so much more.

Now, my opinion is obviously biased since I do not like Rammus. But, with that said, I still feel like Hecarim is easier to play and do well with. The turtle is more situational, and a heck of a lot harder to pull off. But hey, thats just my opinion.

I find it hard to place Hecarim lower than T2 in anything other than Poke/AP. He is such a strong champion.

I guess the way I look at it is Rammus has a higher floor and lower ceiling. Rammus has good damage and tankiness all game. Hecarim has serious choices to make - if you try to rush triforce or gunblade, you're probably going to be too squishy. If you prioritize bulwark and warmogs you don't have the damage rammus does. But once you put those items together, you have a late game monster on Heca.

Caitlyn has not made your list in anyway. Forgive me on some of your opinions, but I'm a firm believer that a Caitlyn of even basic skill level is the single best ranged AD carry in this game mode. Only thing that champion has to do is stay in the far back, and make sure 3 traps are down at all times, they don't even need to be well placed traps. If someone steps on one, your team mates are like omg spam skills free damage.

She was just included in a lumped category:

I have to agree with this, too. I've seen ADC's who just don't get how to position (I swear some of them think they're melee champions?), or they're too afraid to actually contribute anything meaningful during fights. They'll just stand in the back and do nothing, or what amounts to nothing at least. Think a Cait who just casts her ult once and throws out a couple Q's, versus one who actually auto-attacks the whole fight. You lose out on a lot of damage without those AA's.

However, I do feel like Cait should be placed somewhere in the 'Poke' list though.

Also, @OP, you misspelled Kennen.

Yes, I will sit down sometime soon and just do comments on all the ad carries. My issue is different ones are good for different comps, and I don't think they are distinguishable enough to merit different tiers of power. You're right though - Caitlin is probably the lowest skill cap, traps are very useful, and her mana costs are pretty friendly.