Mid and jungle. His kit is too easily countered top after about level 4 by just a chain vest. Mid lane he can have free harass on squishies all day. He's actually a pretty strong counterjungler early since he can use his shadow to surprise enemies or escape like Shaco, along with no mana.

the reason i say he doesnt have an anti-ap kit is cause all anti-mids (kassadin, talon,etc) have a gap closer, silence and burst. Zed doesn't have a silence and his burst is underwhelming. For all the people saying he has free infinite harrass, this is wrong. His Q comes off CD faster than his energy regens at early and mid levels. If you were to throw a Q everytime it came off cooldown you will go energy oom and push the lane pretty hard and his full combo uses about 75% of his energy, factoring in energy regen from shadows, and you cannot full combo someone if you are constantly harrassing. But these are just my observations from playing him, perhaps im am playing his wrong

zed jungle is really strong, very fast clear times and safe, also his ganks are not that bad, what you have to do is ask your laner to initiate, or go out when the enemy commited to the fight, they will have to either forced to use their flash or die with your slows. also you can take exhaust for much stronger ganks, or 1v1

the problem with him is he has no follow up after he ults, enemy can just flash or use a gap closer to escape (cough) kassadin, cait, ez,corki, trist, the list goes on (cough) need to use your ult carefully at the right time :P

Zed's clear time is very fast, no where near "mediocre"

and his ganks are pretty amazing also, you can run in W, and then E to slow down someone, and dish out enough damage for them to blow a flash, or get low enough that they leave lane.

Zed is very good anti-ap mid, rush hexdrinker and you'll win every trade.

Best I've seen was a jungle/counterjungle Zed. He'd get his red, go kill jungler. then he'd gank.His slipperiness makes him really hard to deal with, so once you've really gotten their jungler behind, and their jungle warded, you're playing a 4v5.