That's just counterbuilding, but he does certainly have counterplay!
If he levels Q first (which most if not all Zed players do), don't be afraid of his shadows level four and beyond whenever his Q is on cooldown. Tanking an E or two is fine, it falls off in damage until around level 9, so taking it like a man/woman to win a trade is perfectly fine. Don't tank it willy nilly, though.
While he does have waveclear and some decent aoe, Zed is still primarily a single-target "get in, delete target, get out" kind of guy. Flanking him to make him use his mobility to escape is nice, flanking him after he's used all his mobility options is even nicer.
His ult is a damage amplifier, and the nuke finishes you off. This gives you ample time to react to the mark if he doesn't finish you off beforehand (which you should be able to do if you play smart). If your team has the tools, setting up traps at his shadows is great if you can force him to use the dash function on his ult/W right into a trap (Caitlyn, Teemo, and anyone with traps/picks like Thresh should be able to do this with the right timing).
Bruisers counter him hard.
When flanking him during his ultimate, try not to move too much away from where his shadow spawns. This limits the range of his mobility.
Save your cc for when he gets close to use his passive or a very personal E. Stun him (very fun to do as Ahri, charming just the tip), then walk away and poke his melee ass.
Zed is annoying AF, but playing against and as him I've learned a few tricks.