Battle Moveset

A Good Moveset for Zapdos would have to be this:

Attacks:

Thunderbolt
Hidden Power Ice OR Drill Peck
Agility
Substitute

Items Attached:

Petaya Berry

Preferred Nature:

Modest

Strategy Using Zapdos

Remember to change the EV's to suite your moveset, if you get a good Hidden power, then go with Special attack EV's, if not, then go with HP EV's. This pokemon has been given a poor movepool and is limited with what it can do.
Zapdos type combination allows it for a nice little ground resistance that makes it weak to Rock type attacks. If Zapdos knows Hidden Power Ice/Grass, it has sufficient speed to knock out many Ground/Rock pokemon that you try to use to counter it. The third move was difficult to decide, pondering between Agility and Thunderwave, agility's speed increase stays with Zapdos throughout the entire battle (unless a hazer comes along or is switched out) whereas Thunderwave effects of paralysis stays with your opponent's pokemon till its knocked out.
Substituting is a means of protecting Zapdos from harm, which can be replaced with moves such as Protect. This pokemon has the stats and the type combination that would be useful if it had a better movepool.
If you're unable to obtain Hidden power Ice or grass, then drill peck is another option for a move, since this will gain stab and will deal a lot of damage to many pokemon.

EV Corner:

Max out the EVs in Special Attack & Speed for Zapdos with any remaining in HP

Strategy Against Zapdos

Zapdos, the legendary bird of thunder, is quite possibly the most restricted legendary available (in a similar situation to Moltres), however it isn't without ability. It loses a major weaknesses to Earthquake with its flying secondary type and its secondary type loses its electric weakness due to the combination, giving a nice weakness-resistance ratio of 2-6. It has access to Thunder Wave, which can be one of the most frustrating status's to receive, and has a very high special attack and access to the high powered STAB move Thunderbolt.
- As you can tell, almost all its offensive ability relies on Electric typed moves, and the best way to counter that is with a ground typed Pokémon (although a fast Pokémon with Volt Absorb and Substitute would also be effective, so Jolteon is also a very good counter if it can use Substitute before Zapdos can use Thunder Wave). Almost all Ground types have access to a Rock-typed technique such as Rock Slide, so a Ground type with Rock Slide should suffice to defeat Zapdos. However, you run a risk with using a Ground type against Zapdos since many will carry a Hidden Power of the Grass, Water or Ice type, so be 'tread carefully' when sending out a Ground type slower than Zapdos.
- Another way around Zapdos is to use a 'Special Sponge' (with the technique Mirror Coat) that is more than capable of surviving one of the high powered Thunderbolts and sending back double the received damage, however this is also risky due to Zapdos's access to Drill Peck and an above average attack stat.
- Finally, you could go with a Rock/Ground combination (Rhydon or Golem are the only ones that will reach a final stage of evolution still as Rock/Ground) with a little bit of prediction. If you've tested out the opponents Zapdos to see if they carry Hidden power or not you can safely make an assumption as to whether than can KO you're Rock/Ground Pokémon. Once you've sent out said Pokémon you will most likely get a free turn while your opponent switches to something effective (this turn is best spent using Substitute or something along those lines), or else they'll be stuck using a not very effective Drill Peck (against something with high base defence) or waiting for you to KO them.

Contest Moveset

A good Contest Moveset for Zapdos would have to be this for the Cool Contest best with Lonely, Adament, Naughty or Brave Nature:

Attacks:

Rain Dance
Thunder
Thunderbolt
Hyper Beam

Items Attached:

Red Scarf

Strategy Using Zapdos

If you do the attacks in this following order you should have very few problems; 1st - Rain dance, 2nd - Thunder, 3rd - Rain dance, 4th - Thunderbolt, 5th - Hyperbeam

Locations in Games

Ruby/Sapphire/Emerald Trade from FR/LG Colosseum Trade from FR/LG Fire Red/Leaf Green Power Plant

Animé Appearences

Zapdos has had a few Animé Appearences. First it was on Lightning Island when Lawrence III tried to catch him so he can awake Lugia...it ended up fighting a massive battle between the birds. After that it got drawn to a crystal in Johto and was weak and needed to be healed Movie 2: The Power Of One! Episode 244: As Clear As Crystal!