PHB Tiers - OU Smogon Tiers - OU

Pressure Staller

Zapdos (Calm) @Lum Berry
EVs: 128 HP / 252 Spe / 100 Sp. Def / 28 Def
Substitute
Roost
Hidden Power Grass
Thunderbolt / Metal Sound

With access to Roost and Substitute, you don't have to worry about loosing Zapdos's flying type while behind a Sub. HP Grass is to handle Grounds and Swampert, while Thunderbolt is a good STAB Move. Metal Sound can be used in the place of one of Thunderbolt if your concerned about the lack of Sp. Atk EVs.

Counters

Blissey stops any kind of Special Attacking done by Zapdos cold, and Snorlax to a lesser extent; although both must be careful with the rare Metal Sound user. Regice can do well against sets that do not carry Heat Wave, threatening Zapdos with STAB, super effective Ice Beams. Electivire, Jolteon, and Lanturn can benefit from coming into Thunderbolt or Thunder Wave from Zapdos and get rid of him with their neutral Thunderbolts (or in Lanturn's case, Ice Beam) while Zapdos is stuck to using Heat Wave (in Electivire's and Jolteon's case) or Hidden Power (in Lanturn's case) against them. Other Electrics like Raikou and Ampharos work with this principle as well, but they don't benefit from being Thunderbolted.

Flygon and Gliscor have a relatively easy time against a Zapdos without Hidden Power Ice. Swampert and Rhyperior can wall a Zapdos without Hidden Power Grass. Camerupt does a fair bit of damage to Zapdos with Fire or Rock moves and really only cares about Hidden Power Water. Latias takes little damage from any attack Zapdos can throw at it and Calm Mind away. Grass-types such as Celebi or Meganium can do well against some Zapdos, but the prevalence of Heat Wave and U-turn means they need to watch out. Steelix also does alright against versions that lack Heat Wave, and even boasts an immunity to Toxic.

With Sand Stream boosting its Special Defense, Tyranitar makes an excellent counter, particularly the specially defensive versions. Although Zapdos can conceivably stall out Stone Edge's low PP (Pressure only gives Tyranitar 4 chances to use it), Tyranitar will beat Zapdos by using Crunch. Initially, Crunch approximately breaks even with Roost's healing, but once Tyranitar obtains a Defense drop, it wins the matchup. Regirock in a sandstorm performs similarly, though Tyranitar is more efficient due to its Sand Stream ability.

While walling Zapdos is nice, you will usually need some decent power behind a super effective move to win the war against one with Roost or Rest, because Pressure will bite you. Ice Beam is your best bet against Bold variants, while Ice Punch gives you the best chances against Calm variants. Earthquake helps against Zapdos if it's using Roost.

Credit goes to Smogon for the counters. Thanks Smogon!