To provide some quick thoughts of my own:
: Has seen a lot of changes but effectively got thrown under the bus with the Jinx patch, if I remember correctly. For the most part, it was nerfs to his slow (his only gap closer) and other things like the removal of spell vamp on Vicious Strikes. Put simply, no mobility when compared to top tier picks atm.
: The nerf to the range on his Q when hitting a target marked with E really hurt his viability and was one of the few things keeping him up when he was picked in competitive play. He was propped up almost purely because with the right support, AD carries just couldn't outtrade him and Urgot could kite them with ease, allowing him to win early game and transition into late comfortably. Once Q got his though, Urgot's late game, and even his mid game, is not terribly reliable because his damage isn't that great, and he's hard to fit into a lane.
: Lack of mobility. he needs considerable investment in AP to do damage, but becomes squishy if he does so, and if he builds tanky, he lacks damage. Going tanky AP doesn't really solve either problem.
: Nerfs and not particularly safe to use, even with Zhonya's. Karthus, Morgana, etc. basically do the same thing, but either put out better damage and don't care about dying (Karthus) or are played as support anyways (Morgana).
: Prone to kiting, on top of having a greedy early game with high mana costs.
: Critical chance isn't necessarily reliable and while he trades well in some top lane match ups, he's not that great of a teamfighter.
: Jungle speed is burst based but isn't consistent. As a support, he's only ever been a walking PD buff, which got nerfed some time ago, and with the introduction of Ardent Censer, is even more trivial. His ultimate needs to have a team built around it, when it's much easier to pick a more generic comp that performs better all around.
: Useless passive, not so great top laner, only a decent mid. Once she ult's, she dies pretty fast unless she managed to get fed. Of the melee AD carries, she's pretty much the worst of the bunch, and most of that group has never done well to begin with.
: Easy to catch because of a lack of mobility. Turrets die fast late game, with the exception of his ultimate, which is only a bit tankier. His teamfight can suffer because of this, as his turrets make up the majority of his damage. His poke isn't as strong as other mages, such as Ziggs.
: Effectively outclassed by Ziggs. Also, no mobility.
: He has to build Death Ray's augment, which makes Gravity Field mediocre. Power Transfer has short range. While his ultimate is strong, it's only effective against enemies that can't spread out properly, making it easy to play around it. No mobility.
: One trick pony play pattern that falls off late game. The one trick he's got got nerfed, and it already had a ton of counterplay, in that you could destroy the shield to delete half of his damage. No mobility.
: Stronger assassins exist that aren't nearly as mana dependent.
: Ultimate can be unreliable at times, and he's not remarkable outside of having a passive that can crit on its own base damage. He's effectively an AD carry with a cooldown on his auto attack. Pretty easy to push around early game, especially since he typically goes top.
: Strong if he can get going, but tends to just be annoying and not that threatening. Shrooms got an AP nerf and a competent team will have 3 upgraded oracle lens to take out any shroom that would actually threaten them. Bad teamfighting means he falls off.
: All of her good utility and damage is contained in a pseudo-ultimate, but you can only pick one of them every several seconds. She's just less consistent as a support overall, and her mid/top lane isn't as threatening as Lulu's was whenever she wasn't support.