Fizz is also a pretty good counter as a timely Playful/Trickster can cancel the application of the mark and/or the damage that is applied afterwards.
Annie and Lissandra were mentioned above due to the lockdown they apply as well as the seemingly endless poke they can supply between Annie last hitting with Q she can stay in lane a long time, and Lissandra gets free casts of spells, her Q being her main poke spell.
Supposedly Talon does, I haven't tried it, but Talon's ultimate causes him to go invisible for 2.5 seconds, and the incubation period for Zed to apply extra damage is 3 seconds. So react quickly and you could potentially outburst him. I don't think this would be a hard counter, but perhaps more of a skill matchup.
LeBlanc would likely go even as well assuming you can save a portion of your mobility to convince him to tower dive jump back and chain him under turret.
Malzahar could potentially work as well because your ultimate is full suppression, just drop the combo on top of yourself and ult him when he shows up again. He doesn't apply any more damage, and will often times be dead or nearly dead. Remember his W at rank 5 does a minimum of 40% of their maximum hp in damage factor in 300-400AP and that's an additional 15-20% of their maximum hp over 4 seconds, in combination with a Q, an E, or both, and your ultimate, you blow up just about anyone in a matter of seconds.
I've also seen Heimer do okay with proper ultimate and stun grenade usage, but this one is less reliable obviously.
The issue of Zed will likely come down largely to the experience of the Zed player, I'm not going to deathmark you until you're at least down to half health unless I know you don't have much to defend against it, and I can easily apply the necessary damage and leave.