Due to the fact that I started Pokémon with Sapphire, I naturally became attached to both Kyogre and Rayquaza. However, in the event of losing Kyogre in a memory crash in the Emerald I transferred it into, I was left with Rayquaza. I always appreciated his special ability to remove any weather condition that Groudon, Kyogre or any weather-based attack would induce. Such a capability allowed double battles to be just a little bit easier.
Aside from his assistance in double battles, Rayquaza can very easily hold his ground in a regular battle. As a legendary, he has great stats and powerful attacks. This deadly combination can leave even the strongest opponents defeated.
Aside from overall effectiveness, I've always loved his background. There aren't many legendary Pokémon that reside in the Ozone layer of the atmosphere. This tiny tidbit of information that may be overlooked by other people, but I've remembered it, even though I haven't picked up Sapphire in nearly 4 years.
And yet, his appearance is also one of the reasons I like him so much. His long, snake-like body is not common among the legendary Pokémon. Unlike many other legendary Pokémon, he may be long, but he isn't a massive Pokémon that could easily crush a smaller one with their feet alone. Rayquaza's physical make up provides more agility than just pure brute force.
There are so many other reasons why Rayquaza is my favorite legendary, but these were just a few. I have so many memories with him, even though I was forced to defeat the one in Sky Pillar (I forgot to save right before) and had to acquire him through a gameshark. He's more than just another Pokémon I went through a lot of trouble to catch, it was a joy to capture him.