Battle Moveset

A Good Special Sweeper Moveset for Rayquaza would have to be this:

Attacks:

Dragon Claw
Flamethrower
Ice Beam
Surf

Items Attached:

Salac Berry

Preferred Nature:

Timid

Strategy Using Rayquaza

So much can be said about Rayquaza, it has incredible offensive stats, both attack and special attack have a base stat of 150, which almost rivals Mewtwo's special attack strength.
Rayquaza can be used as either a special sweeper or physical sweeper. This is the special sweeper moveset, and of course, replace any move you want with another of the special attacks available to it, e.g Thunderbolt.
However, like most dragon pokemon, Rayquaza has a 4x weakness to ice, and with Ice beam being quite a popular move, be prepared for your opponent to use ice beam on Rayquaza. As for the moveset, this is simple sweeping moves and use them to your advantage, Dragon claw gains STAB too. The nature and max EV's into speed will increase Rayquaza's speed, which is often needed in battles. The Salac battle will also increase Rayquaza's speed when its HP becomes low.
If you wish Rayquaza to be a physical sweeper, then I suggest this moveset: Dragon dance, Aerial ace, Extremespeed, Earthquake, and yet again, you could replace one of these moves for another one available to Rayquaza.
Overall, Rayquaza has great stats, a wide movepool and is a very powerful pokemon. This pokemon isn't to be taken lightly, it could easily out sweep your team with the speed increasing move available to it.

EV Corner:

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

Strategy Against Rayquaza

Rayquaza has strong Defense & Special Defense...and they are both equal so your best bet here is to go at it with Super Effective Attacks. Dragon type would do nicely but Ice would knock this Pokémon back into the O-Zone Layer in a huge Ice Block with 0HP

Contest Moveset

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

Attacks:

Rain Dance
Thunder
Thunderbolt
Outrage

Items Attached:

Red Scarf

Strategy Using Rayquaza

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

Locations in Games

Ruby/Sapphire Sky Pillar Colosseum Trade from R/S Fire Red/Leaf Green Trade from R/S

Animé Appearences

Rayquaza has had one Animé Appearence. While it was high up in the sky a Meteor flew straight past it almost hitting it, after following Rayquaza found a Deoxys and started a battle with it. Movie 7: Visitor Of The Space Fissure!