Latias/Latios
Method of Catching Latios/Latias
Requirements:
-Acro Bike
-At least 1 Defeat of the Elite 4
-At least 1 Max Repel
-Something hard and heavy that you can place on a single button of your GameBoy:P
Method:
Here's what you do. After you've defeated the E4, go to any patch of grass (really, it doesn't matter where) in Hoenn and use your Max Repel. Equip your Acro Bike. Then, place your heavy object on your Game Boy in such a way that it holds down only the B button. Watch the screen and make sure that your character is bunny hopping, but is remaining in the same spot. He is? Great. Now leave your Game Boy alone for an hour or two. No, I'm not kidding. Go away for a good long while, and then come back. Don't bother watching, 'cause this method usually takes time to work. Anyway, when you come back, you (Should) have run into Latios/Latias.
Here's why it works:
Latias/Latios works in much the same way that the Legendary dogs did in G/S/C. He/She changes regions frequently, and will do so even if you stay in one region all the time. This method works on the theory that, if you wait in one region long enough, he/she'll eventually meander into it, and then you'll encounter the wily Pokemon. The Max Repel will keep other Pokemon away from you, and the bunny hopping simulates walking through the grass without wasting steps and exhausting your Max Repel.
So now you should have run into the elusive Latios/Latias. What happens next is up to you. I always used a master ball, because I hate chasing them around. But if you want to do it the hard way, just remember that once you've run into Latios/Latias, you can track him/her using the same method as the one used on the Legendary dogs - look at the area page for that Pokemon in your 'Dex. It'll show the current location of him/her. Of course, this is provided you don't make him/her faint. That's it, people. Happy hunting!